1.
International System of Units
–
The International System of Units is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, the system also establishes a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system was published in 1960 as the result of an initiative began in 1948. It is based on the system of units rather than any variant of the centimetre-gram-second system. The motivation for the development of the SI was the diversity of units that had sprung up within the CGS systems, the International System of Units has been adopted by most developed countries, however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the metre and kilogram as standards of length, in the 1830s Carl Friedrich Gauss laid the foundations for a coherent system based on length, mass, and time. In the 1860s a group working under the auspices of the British Association for the Advancement of Science formulated the requirement for a coherent system of units with base units and derived units. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram, in 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, kelvin, in 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 July 1792, the proposed the names metre, are, litre and grave for the units of length, area, capacity. The committee also proposed that multiples and submultiples of these units were to be denoted by decimal-based prefixes such as centi for a hundredth, on 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the magnetic field had only been described in relative terms. The technique used by Gauss was to equate the torque induced on a magnet of known mass by the earth’s magnetic field with the torque induced on an equivalent system under gravity. The resultant calculations enabled him to assign dimensions based on mass, length, a French-inspired initiative for international cooperation in metrology led to the signing in 1875 of the Metre Convention. Initially the convention only covered standards for the metre and the kilogram, one of each was selected at random to become the International prototype metre and International prototype kilogram that replaced the mètre des Archives and kilogramme des Archives respectively. Each member state was entitled to one of each of the prototypes to serve as the national prototype for that country. Initially its prime purpose was a periodic recalibration of national prototype metres. The official language of the Metre Convention is French and the version of all official documents published by or on behalf of the CGPM is the French-language version

International System of Units
–
Stone marking the

Austro-Hungarian /Italian border at

Pontebba displaying

myriametres, a unit of 10 km used in

Central Europe in the 19th century (but since

deprecated).

International System of Units
–
The seven base units in the International System of Units

International System of Units
–

Carl Friedrich Gauss
International System of Units
–

Thomson
2.
SI base unit
–
The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science, thus, the kelvin, named after Lord Kelvin, has the symbol K and the ampere, named after André-Marie Ampère, has the symbol A. Many other units, such as the litre, are not part of the SI. The definitions of the units have been modified several times since the Metre Convention in 1875. Since the redefinition of the metre in 1960, the kilogram is the unit that is directly defined in terms of a physical artifact. However, the mole, the ampere, and the candela are linked through their definitions to the mass of the platinum–iridium cylinder stored in a vault near Paris. It has long been an objective in metrology to define the kilogram in terms of a fundamental constant, two possibilities have attracted particular attention, the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011

SI base unit
–
The seven SI base units and the interdependency of their definitions: for example, to extract the definition of the metre from the

speed of light, the definition of the second must be known while the

ampere and

candela are both dependent on the definition of

energy which in turn is defined in terms of

length,

mass and

time.

3.
Ampere
–
The ampere, often shortened to amp, is a unit of electric current. In the International System of Units the ampere is one of the seven SI base units and it is named after André-Marie Ampère, French mathematician and physicist, considered the father of electrodynamics. SI defines the ampere in terms of base units by measuring the electromagnetic force between electrical conductors carrying electric current. The ampere was then defined as one coulomb of charge per second, in SI, the unit of charge, the coulomb, is defined as the charge carried by one ampere during one second. In the future, the SI definition may shift back to charge as the base unit, ampères force law states that there is an attractive or repulsive force between two parallel wires carrying an electric current. This force is used in the definition of the ampere. The SI unit of charge, the coulomb, is the quantity of electricity carried in 1 second by a current of 1 ampere, conversely, a current of one ampere is one coulomb of charge going past a given point per second,1 A =1 C s. In general, charge Q is determined by steady current I flowing for a time t as Q = It, constant, instantaneous and average current are expressed in amperes and the charge accumulated, or passed through a circuit over a period of time is expressed in coulombs. The relation of the ampere to the coulomb is the same as that of the watt to the joule, the ampere was originally defined as one tenth of the unit of electric current in the centimetre–gram–second system of units. That unit, now known as the abampere, was defined as the amount of current that generates a force of two dynes per centimetre of length between two wires one centimetre apart. The size of the unit was chosen so that the derived from it in the MKSA system would be conveniently sized. The international ampere was a realization of the ampere, defined as the current that would deposit 0.001118 grams of silver per second from a silver nitrate solution. Later, more accurate measurements revealed that this current is 0.99985 A, at present, techniques to establish the realization of an ampere have a relative uncertainty of approximately a few parts in 107, and involve realizations of the watt, the ohm and the volt. Rather than a definition in terms of the force between two current-carrying wires, it has proposed that the ampere should be defined in terms of the rate of flow of elementary charges. Since a coulomb is equal to 6. 2415093×1018 elementary charges. The proposed change would define 1 A as being the current in the direction of flow of a number of elementary charges per second. In 2005, the International Committee for Weights and Measures agreed to study the proposed change, the new definition was discussed at the 25th General Conference on Weights and Measures in 2014 but for the time being was not adopted. The current drawn by typical constant-voltage energy distribution systems is usually dictated by the power consumed by the system, for this reason the examples given below are grouped by voltage level

Ampere
–
Demonstration model of a moving iron ammeter. As the current through the coil increases, the plunger is drawn further into the coil and the pointer deflects to the right.

4.
Candela
–
The candela is the SI base unit of luminous intensity, that is, luminous power per unit solid angle emitted by a point light source in a particular direction. A common candle emits light with an intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the word candela means candle in Latin. Like most other SI base units, the candela has an operational definition—it is defined by a description of a process that will produce one candela of luminous intensity. The definition describes how to produce a source that emits one candela. Such a source could then be used to calibrate instruments designed to measure luminous intensity, the candela is sometimes still called by the old name candle, such as in foot-candle and the modern definition of candlepower. The frequency chosen is in the spectrum near green, corresponding to a wavelength of about 555 nanometres. The human eye is most sensitive to frequency, when adapted for bright conditions. At other frequencies, more radiant intensity is required to achieve the same luminous intensity, if more than one wavelength is present, one must sum or integrate over the spectrum of wavelengths present to get the total luminous intensity. A common candle emits light with roughly 1 cd luminous intensity. A25 W compact fluorescent light bulb puts out around 1700 lumens, if light is radiated equally in all directions. Focused into a 20° beam, the light bulb would have an intensity of around 18,000 cd. The luminous intensity of light-emitting diodes is measured in millicandelas, or thousandths of a candela, indicator LEDs are typically in the 50 mcd range, ultra-bright LEDs can reach 15,000 mcd, or higher. Prior to 1948, various standards for luminous intensity were in use in a number of countries and these were typically based on the brightness of the flame from a standard candle of defined composition, or the brightness of an incandescent filament of specific design. One of the best-known of these was the English standard of candlepower, one candlepower was the light produced by a pure spermaceti candle weighing one sixth of a pound and burning at a rate of 120 grains per hour. Germany, Austria and Scandinavia used the Hefnerkerze, a based on the output of a Hefner lamp. It became clear that a unit was needed. Jules Violle had proposed a standard based on the emitted by 1 cm2 of platinum at its melting point

Candela
–

Photopic (black) and

scotopic (green) luminosity functions. The photopic includes the CIE 1931 standard (solid), the Judd–Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data (dotted). The horizontal axis is wavelength in nm.

5.
Kelvin
–
The kelvin is a unit of measure for temperature based upon an absolute scale. It is one of the seven units in the International System of Units and is assigned the unit symbol K. The kelvin is defined as the fraction 1⁄273.16 of the temperature of the triple point of water. In other words, it is defined such that the point of water is exactly 273.16 K. The Kelvin scale is named after the Belfast-born, Glasgow University engineer and physicist William Lord Kelvin, unlike the degree Fahrenheit and degree Celsius, the kelvin is not referred to or typeset as a degree. The kelvin is the unit of temperature measurement in the physical sciences, but is often used in conjunction with the Celsius degree. The definition implies that absolute zero is equivalent to −273.15 °C, Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale, when spelled out or spoken, the unit is pluralised using the same grammatical rules as for other SI units such as the volt or ohm. When reference is made to the Kelvin scale, the word kelvin—which is normally a noun—functions adjectivally to modify the noun scale and is capitalized, as with most other SI unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967–1968, the unit kelvin was called a degree and it was distinguished from the other scales with either the adjective suffix Kelvin or with absolute and its symbol was °K. The latter term, which was the official name from 1948 until 1954, was ambiguous since it could also be interpreted as referring to the Rankine scale. Before the 13th CGPM, the form was degrees absolute. The 13th CGPM changed the name to simply kelvin. Its measured value was 0.01028 °C with an uncertainty of 60 µK, the use of SI prefixed forms of the degree Celsius to express a temperature interval has not been widely adopted. In 2005 the CIPM embarked on a program to redefine the kelvin using a more experimentally rigorous methodology, the current definition as of 2016 is unsatisfactory for temperatures below 20 K and above 1300 K. In particular, the committee proposed redefining the kelvin such that Boltzmanns constant takes the exact value 1. 3806505×10−23 J/K, from a scientific point of view, this will link temperature to the rest of SI and result in a stable definition that is independent of any particular substance. From a practical point of view, the redefinition will pass unnoticed, the kelvin is often used in the measure of the colour temperature of light sources. Colour temperature is based upon the principle that a black body radiator emits light whose colour depends on the temperature of the radiator, black bodies with temperatures below about 4000 K appear reddish, whereas those above about 7500 K appear bluish

Kelvin
–

Lord Kelvin, the namesake of the unit

Kelvin
–
A thermometer calibrated in degrees Celsius (left) and kelvins (right).

6.
Kilogram
–
The kilogram or kilogramme is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype of the Kilogram. The avoirdupois pound, used in both the imperial and US customary systems, is defined as exactly 0.45359237 kg, making one kilogram approximately equal to 2.2046 avoirdupois pounds. Other traditional units of weight and mass around the world are also defined in terms of the kilogram, the gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimeter of water at the melting point of ice. The final kilogram, manufactured as a prototype in 1799 and from which the IPK was derived in 1875, had an equal to the mass of 1 dm3 of water at its maximum density. The kilogram is the only SI base unit with an SI prefix as part of its name and it is also the only SI unit that is still directly defined by an artifact rather than a fundamental physical property that can be reproduced in different laboratories. Three other base units and 17 derived units in the SI system are defined relative to the kilogram, only 8 other units do not require the kilogram in their definition, temperature, time and frequency, length, and angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, the decision was originally deferred until 2014, in 2014 it was deferred again until the next meeting. There are currently several different proposals for the redefinition, these are described in the Proposed Future Definitions section below, the International Prototype Kilogram is rarely used or handled. In the decree of 1795, the term gramme thus replaced gravet, the French spelling was adopted in the United Kingdom when the word was used for the first time in English in 1797, with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with kilogram having become by far the more common, UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has used to mean both kilogram and kilometer. In 1935 this was adopted by the IEC as the Giorgi system, now known as MKS system. In 1948 the CGPM commissioned the CIPM to make recommendations for a practical system of units of measurement. This led to the launch of SI in 1960 and the subsequent publication of the SI Brochure, the kilogram is a unit of mass, a property which corresponds to the common perception of how heavy an object is. Mass is a property, that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor, they are weightless. However, since objects in microgravity still retain their mass and inertia, the ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. On April 7,1795, the gram was decreed in France to be the weight of a volume of pure water equal to the cube of the hundredth part of the metre

Kilogram
–
A domestic-quality one-kilogram weight made of

cast iron (the

credit card is for scale). The shape follows

OIML recommendation R52 for cast-iron hexagonal weights

Kilogram
–
Measurement of weight – gravitational attraction of the measurand causes a distortion of the spring

Kilogram
–
Measurement of mass – the gravitational force on the measurand is balanced against the gravitational force on the weights.

Kilogram
–
The Arago kilogram, an exact copy of the "Kilogramme des Archives" commissioned in 1821 by the US under supervision of French physicist

François Arago that served as the US's first kilogram standard of mass until 1889, when the US converted to primary metric standards and received its current kilogram prototypes, K4 and K20.

7.
Metre
–
The metre or meter, is the base unit of length in the International System of Units. The metre is defined as the length of the path travelled by light in a vacuum in 1/299792458 seconds, the metre was originally defined in 1793 as one ten-millionth of the distance from the equator to the North Pole. In 1799, it was redefined in terms of a metre bar. In 1960, the metre was redefined in terms of a number of wavelengths of a certain emission line of krypton-86. In 1983, the current definition was adopted, the imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, Metre is the standard spelling of the metric unit for length in nearly all English-speaking nations except the United States and the Philippines, which use meter. Measuring devices are spelled -meter in all variants of English, the suffix -meter has the same Greek origin as the unit of length. This range of uses is found in Latin, French, English. Thus calls for measurement and moderation. In 1668 the English cleric and philosopher John Wilkins proposed in an essay a decimal-based unit of length, as a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. In 1668, Wilkins proposed using Christopher Wrens suggestion of defining the metre using a pendulum with a length which produced a half-period of one second, christiaan Huygens had observed that length to be 38 Rijnland inches or 39.26 English inches. This is the equivalent of what is now known to be 997 mm, no official action was taken regarding this suggestion. In the 18th century, there were two approaches to the definition of the unit of length. One favoured Wilkins approach, to define the metre in terms of the length of a pendulum which produced a half-period of one second. The other approach was to define the metre as one ten-millionth of the length of a quadrant along the Earths meridian, that is, the distance from the Equator to the North Pole. This means that the quadrant would have defined as exactly 10000000 metres at that time. To establish a universally accepted foundation for the definition of the metre, more measurements of this meridian were needed. This portion of the meridian, assumed to be the length as the Paris meridian, was to serve as the basis for the length of the half meridian connecting the North Pole with the Equator

Metre
–

Belfry, Dunkirk —the northern end of the meridian arc

Metre

Metre
–

Fortress of Montjuïc —the southerly end of the meridian arc

Metre
–
Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray

8.
Mole (unit)
–
The mole is the unit of measurement in the International System of Units for amount of substance. This number is expressed by the Avogadro constant, which has a value of 6. 022140857×1023 mol−1, the mole is one of the base units of the SI, and has the unit symbol mol. The mole is used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2 H2 + O2 →2 H2O implies that 2 moles of dihydrogen and 1 mole of dioxygen react to form 2 moles of water. The mole may also be used to express the number of atoms, ions, the concentration of a solution is commonly expressed by its molarity, defined as the number of moles of the dissolved substance per litre of solution. For example, the relative molecular mass of natural water is about 18.015, therefore. The term gram-molecule was formerly used for essentially the same concept, the term gram-atom has been used for a related but distinct concept, namely a quantity of a substance that contains Avogadros number of atoms, whether isolated or combined in molecules. Thus, for example,1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2, in honor of the unit, some chemists celebrate October 23, which is a reference to the 1023 scale of the Avogadro constant, as Mole Day. Some also do the same for February 6 and June 2, thus, by definition, one mole of pure 12C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the number of molecules as X moles of any other substance. The mass per mole of a substance is called its molar mass, the number of elementary entities in a sample of a substance is technically called its amount. Therefore, the mole is a convenient unit for that physical quantity, one can determine the chemical amount of a known substance, in moles, by dividing the samples mass by the substances molar mass. Other methods include the use of the volume or the measurement of electric charge. The mass of one mole of a substance depends not only on its molecular formula, since the definition of the gram is not mathematically tied to that of the atomic mass unit, the number NA of molecules in a mole must be determined experimentally. The value adopted by CODATA in 2010 is NA =6. 02214129×1023 ±0. 00000027×1023, in 2011 the measurement was refined to 6. 02214078×1023 ±0. 00000018×1023. The number of moles of a sample is the sample mass divided by the mass of the material. The history of the mole is intertwined with that of mass, atomic mass unit, Avogadros number. The first table of atomic mass was published by John Dalton in 1805

Mole (unit)
–

Base units
9.
Second
–
The second is the base unit of time in the International System of Units. It is qualitatively defined as the division of the hour by sixty. SI definition of second is the duration of 9192631770 periods of the corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Seconds may be measured using a mechanical, electrical or an atomic clock, SI prefixes are combined with the word second to denote subdivisions of the second, e. g. the millisecond, the microsecond, and the nanosecond. Though SI prefixes may also be used to form multiples of the such as kilosecond. The second is also the unit of time in other systems of measurement, the centimetre–gram–second, metre–kilogram–second, metre–tonne–second. Absolute zero implies no movement, and therefore zero external radiation effects, the second thus defined is consistent with the ephemeris second, which was based on astronomical measurements. The realization of the second is described briefly in a special publication from the National Institute of Standards and Technology. 1 international second is equal to, 1⁄60 minute 1⁄3,600 hour 1⁄86,400 day 1⁄31,557,600 Julian year 1⁄, more generally, = 1⁄, the Hellenistic astronomers Hipparchus and Ptolemy subdivided the day into sixty parts. They also used an hour, simple fractions of an hour. No sexagesimal unit of the day was used as an independent unit of time. The modern second is subdivided using decimals - although the third remains in some languages. The earliest clocks to display seconds appeared during the last half of the 16th century, the second became accurately measurable with the development of mechanical clocks keeping mean time, as opposed to the apparent time displayed by sundials. The earliest spring-driven timepiece with a hand which marked seconds is an unsigned clock depicting Orpheus in the Fremersdorf collection. During the 3rd quarter of the 16th century, Taqi al-Din built a clock with marks every 1/5 minute, in 1579, Jost Bürgi built a clock for William of Hesse that marked seconds. In 1581, Tycho Brahe redesigned clocks that displayed minutes at his observatory so they also displayed seconds, however, they were not yet accurate enough for seconds. In 1587, Tycho complained that his four clocks disagreed by plus or minus four seconds, in 1670, London clockmaker William Clement added this seconds pendulum to the original pendulum clock of Christiaan Huygens. From 1670 to 1680, Clement made many improvements to his clock and this clock used an anchor escapement mechanism with a seconds pendulum to display seconds in a small subdial

Second
–
FOCS 1, a continuous cold caesium fountain atomic clock in Switzerland, started operating in 2004 at an uncertainty of one second in 30 million years.

Second
–
Key concepts

10.
SI derived unit
–
The International System of Units specifies a set of seven base units from which all other SI units of measurement are derived. Each of these units is either dimensionless or can be expressed as a product of powers of one or more of the base units. For example, the SI derived unit of area is the metre. The degree Celsius has an unclear status, and is arguably an exception to this rule. The names of SI units are written in lowercase, the symbols for units named after persons, however, are always written with an uppercase initial letter. In addition to the two dimensionless derived units radian and steradian,20 other derived units have special names, some other units such as the hour, litre, tonne, bar and electronvolt are not SI units, but are widely used in conjunction with SI units. Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned, International System of Quantities International System of Units International Vocabulary of Metrology Metric prefix Metric system Non-SI units mentioned in the SI Planck units SI base unit I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC, Quantities, Units and Symbols in Physical Chemistry. CS1 maint, Multiple names, authors list

SI derived unit
–

Base units
11.
Becquerel
–
The becquerel is the SI derived unit of radioactivity. One becquerel is defined as the activity of a quantity of material in which one nucleus decays per second. The becquerel is therefore equivalent to a second, s−1. The becquerel is named after Henri Becquerel, who shared a Nobel Prize in Physics with Pierre, as with every International System of Units unit named for a person, the first letter of its symbol is uppercase. 1 Bq =1 s−1 A special name was introduced for the second to represent radioactivity to avoid potentially dangerous mistakes with prefixes. For example,1 µs−1 could be taken to mean 106 disintegrations per second, other names considered were hertz, a special name already in use for the reciprocal second, and fourier. The hertz is now used for periodic phenomena. Whereas 1 Hz is 1 cycle per second,1 Bq is 1 aperiodic radioactivity event per second, the gray and the becquerel were introduced in 1975. Between 1953 and 1975, absorbed dose was often measured in rads, decay activity was measured in curies before 1946 and often in rutherfords between 1946 and 1975. Like any SI unit, Bq can be prefixed, commonly used multiples are kBq, MBq, GBq, TBq, for practical applications,1 Bq is a small unit, therefore, the prefixes are common. For example, the roughly 0.0169 g of potassium-40 present in a human body produces approximately 4,400 disintegrations per second or 4.4 kBq of activity. The global inventory of carbon-14 is estimated to be 8. 5×1018 Bq, the nuclear explosion in Hiroshima is estimated to have produced 8×1024 Bq. The becquerel succeeded the curie, an older, non-SI unit of radioactivity based on the activity of 1 gram of radium-226, the curie is defined as 3. 7·1010 s−1, or 37 GBq. The following table shows radiation quantities in SI and non-SI units

Becquerel
–
Graphic showing relationships between radioactivity and detected ionizing radiation

12.
Coulomb
–
The coulomb is the International System of Units unit of electric charge. 242×1018 protons, and −1 C is equivalent to the charge of approximately 6. 242×1018 electrons. This SI unit is named after Charles-Augustin de Coulomb, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, the SI system defines the coulomb in terms of the ampere and second,1 C =1 A ×1 s. The second is defined in terms of a frequency emitted by caesium atoms. The ampere is defined using Ampères force law, the definition relies in part on the mass of the prototype kilogram. In practice, the balance is used to measure amperes with the highest possible accuracy. One coulomb is the magnitude of charge in 6. 24150934×10^18 protons or electrons. The inverse of this gives the elementary charge of 1. 6021766208×10−19 C. The magnitude of the charge of one mole of elementary charges is known as a faraday unit of charge. In terms of Avogadros number, one coulomb is equal to approximately 1.036 × NA×10−5 elementary charges, one ampere-hour =3600 C,1 mA⋅h =3.6 C. One statcoulomb, the obsolete CGS electrostatic unit of charge, is approximately 3. 3356×10−10 C or about one-third of a nanocoulomb, the elementary charge, the charge of a proton, is approximately 1. 6021766208×10−19 C. In SI, the charge in coulombs is an approximate value. However, in other systems, the elementary charge has an exact value by definition. Specifically, e90 = / C exactly, SI itself may someday change its definitions in a similar way. For example, one possible proposed redefinition is the ampere. is such that the value of the charge e is exactly 1. 602176487×10−19 coulombs. This proposal is not yet accepted as part of the SI, the charges in static electricity from rubbing materials together are typically a few microcoulombs. The amount of charge that travels through a lightning bolt is typically around 15 C, the amount of charge that travels through a typical alkaline AA battery from being fully charged to discharged is about 5 kC =5000 C ≈1400 mA⋅h. The hydraulic analogy uses everyday terms to illustrate movement of charge, the analogy equates charge to a volume of water, and voltage to pressure

Coulomb
–

Base units
13.
Celsius
–
Celsius, also known as centigrade, is a metric scale and unit of measurement for temperature. As an SI derived unit, it is used by most countries in the world and it is named after the Swedish astronomer Anders Celsius, who developed a similar temperature scale. The degree Celsius can refer to a temperature on the Celsius scale as well as a unit to indicate a temperature interval. Before being renamed to honour Anders Celsius in 1948, the unit was called centigrade, from the Latin centum, which means 100, and gradus, which means steps. The scale is based on 0° for the point of water. This scale is widely taught in schools today, by international agreement the unit degree Celsius and the Celsius scale are currently defined by two different temperatures, absolute zero, and the triple point of VSMOW. This definition also precisely relates the Celsius scale to the Kelvin scale, absolute zero, the lowest temperature possible, is defined as being precisely 0 K and −273.15 °C. The temperature of the point of water is defined as precisely 273.16 K at 611.657 pascals pressure. This definition fixes the magnitude of both the degree Celsius and the kelvin as precisely 1 part in 273.16 of the difference between absolute zero and the point of water. Thus, it sets the magnitude of one degree Celsius and that of one kelvin as exactly the same, additionally, it establishes the difference between the two scales null points as being precisely 273.15 degrees. In his paper Observations of two persistent degrees on a thermometer, he recounted his experiments showing that the point of ice is essentially unaffected by pressure. He also determined with precision how the boiling point of water varied as a function of atmospheric pressure. He proposed that the point of his temperature scale, being the boiling point. This pressure is known as one standard atmosphere, the BIPMs 10th General Conference on Weights and Measures later defined one standard atmosphere to equal precisely 1013250dynes per square centimetre. On 19 May 1743 he published the design of a mercury thermometer, in 1744, coincident with the death of Anders Celsius, the Swedish botanist Carolus Linnaeus reversed Celsiuss scale. In it, Linnaeus recounted the temperatures inside the orangery at the University of Uppsala Botanical Garden, since the 19th century, the scientific and thermometry communities worldwide referred to this scale as the centigrade scale. Temperatures on the scale were often reported simply as degrees or. More properly, what was defined as centigrade then would now be hectograde.2 gradians, for scientific use, Celsius is the term usually used, with centigrade otherwise continuing to be in common but decreasing use, especially in informal contexts in English-speaking countries

Celsius
–
A

thermometer calibrated in degrees Celsius

14.
Farad
–
The farad is the SI derived unit of electrical capacitance, the ability of a body to store an electrical charge. It is named after the English physicist Michael Faraday, one farad is defined as the capacitance across which, when charged with one coulomb, there is a potential difference of one volt. Equally, one farad can be described as the capacitance which stores a one-coulomb charge across a potential difference of one volt, the relationship between capacitance, charge and potential difference is linear. For example, if the difference across a capacitor is halved. For most applications, the farad is a large unit of capacitance. Most electrical and electronic applications are covered by the following SI prefixes,1 mF =1000 μF =1000000 nF1 μF =0.000001 F =1000 nF =1000000 pF1 nF =0. In 1881 at the International Congress of Electricians in Paris, the name farad was officially used for the unit of electrical capacitance, a capacitor consists of two conducting surfaces, frequently referred to as plates, separated by an insulating layer usually referred to as a dielectric. The original capacitor was the Leyden jar developed in the 18th century and it is the accumulation of electric charge on the plates that results in capacitance. Values of capacitors are specified in farads, microfarads, nanofarads and picofarads. The millifarad is rarely used in practice, while the nanofarad is uncommon in North America, the size of commercially available capacitors ranges from around 0.1 pF to 5000F supercapacitors. Capacitance values of 1 pF or lower can be achieved by twisting two short lengths of insulated wire together, the capacitance of the Earths ionosphere with respect to the ground is calculated to be about 1 F. The picofarad is sometimes pronounced as puff or pic, as in a ten-puff capacitor. Similarly, mic is sometimes used informally to signify microfarads, if the Greek letter μ is not available, the notation uF is often used as a substitute for μF in electronics literature. A micro-microfarad, an obsolete unit sometimes found in texts, is the equivalent of a picofarad. In texts prior to 1960, and on capacitor packages even more recently. Similarly, mmf or MMFD represented picofarads, the reciprocal of capacitance is called electrical elastance, the unit of which is the daraf. The abfarad is an obsolete CGS unit of equal to 109 farads. The statfarad is a rarely used CGS unit equivalent to the capacitance of a capacitor with a charge of 1 statcoulomb across a potential difference of 1 statvolt and it is 1/ farad, approximately 1.1126 picofarads

Farad
–
A comparatively small 1 farad capacitor, for low voltages and current transfers

Farad
–
Examples of different types of capacitors

15.
Gray (unit)
–
The gray is a derived unit of ionizing radiation dose in the International System of Units. It is defined as the absorption of one joule of energy per kilogram of matter. It is used as a measure of absorbed dose, specific energy and it is a physical quantity, and does not take into account any biological context. Unlike the pre-1971 non-SI roentgen unit of exposure, the gray when used for absorbed dose is defined independently of any target material. However, when measuring kerma the reference target material must be defined explicitly, usually as dry air at standard temperature and pressure. The corresponding cgs unit, the rad, remains common in the United States, though strongly discouraged in the guide for U. S. National Institute of Standards. The gray was named after British physicist Louis Harold Gray, a pioneer in the measurement of X-ray and radium radiation and it was adopted as part of the International System of Units in 1975. One gray is the absorption of one joule of energy, in the form of ionizing radiation, measuring and controlling the value of absorbed dose is vital to ensuring correct operation of these processes. Kerma is a measure of the energy of ionisation due to irradiation. Importantly, kerma dose is different from absorbed dose, depending on the energies involved. The measurement of absorbed dose is a problem, and so many different dosimeters are available for these measurements. These dosimeters cover measurements that can be done in 1-D, 2-D and 3-D, in radiation therapy, the amount of radiation applied varies depending on the type and stage of cancer being treated. For curative cases, the dose for a solid epithelial tumor ranges from 60 to 80 Gy. Preventive doses are typically around 45–60 Gy in 1. 8–2 Gy fractions, the absorbed dose also plays an important role in radiation protection, as it is the starting point for calculating the effect of low levels of radiation. In radiation protection dose assessment, the health risk is defined as the probability of cancer induction. This probability is related to the equivalent dose in sieverts, which has the dimensions as the gray. It is related to the gray by weighting factors described in the articles on equivalent dose, to avoid any risk of confusion between the absorbed dose and the equivalent dose, the absorbed dose is stated in grays and the equivalent dose is stated in sieverts. The accompanying diagrams show how absorbed dose is first obtained by computational techniques, radiation poisoning - The gray is conventionally used to express the severity of what are known as tissue effects from doses received in acute exposure to high levels of ionizing radiation

Gray (unit)
–
External dose quantities used in radiation protection and dosimetry

16.
Henry (unit)
–
The henry is the SI derived unit of electrical inductance. The unit is named after Joseph Henry, the American scientist who discovered electromagnetic induction independently of, the magnetic permeability of vacuum is 4π × 10−7 H⋅m−1. The henry is a unit based on four of the seven base units of the International System of Units, kilogram, meter, second. The United States National Institute of Standards and Technology recommends English-speaking users of SI to write the plural as henries

Henry (unit)
–
An

inductor composed of a

wire wound around a

magnetic core used to confine and guide the induced

magnetic field.

Henry (unit)
–

Base units
17.
Hertz
–
The hertz is the unit of frequency in the International System of Units and is defined as one cycle per second. It is named for Heinrich Rudolf Hertz, the first person to provide proof of the existence of electromagnetic waves. Hertz are commonly expressed in SI multiples kilohertz, megahertz, gigahertz, kilo means thousand, mega meaning million, giga meaning billion and tera for trillion. Some of the units most common uses are in the description of waves and musical tones, particularly those used in radio-. It is also used to describe the speeds at which computers, the hertz is equivalent to cycles per second, i. e. 1/second or s −1. In English, hertz is also used as the plural form, as an SI unit, Hz can be prefixed, commonly used multiples are kHz, MHz, GHz and THz. One hertz simply means one cycle per second,100 Hz means one hundred cycles per second, and so on. The unit may be applied to any periodic event—for example, a clock might be said to tick at 1 Hz, the rate of aperiodic or stochastic events occur is expressed in reciprocal second or inverse second in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second,1 Bq is 1 aperiodic radionuclide event per second, the conversion between a frequency f measured in hertz and an angular velocity ω measured in radians per second is ω =2 π f and f = ω2 π. This SI unit is named after Heinrich Hertz, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, the hertz is named after the German physicist Heinrich Hertz, who made important scientific contributions to the study of electromagnetism. The name was established by the International Electrotechnical Commission in 1930, the term cycles per second was largely replaced by hertz by the 1970s. One hobby magazine, Electronics Illustrated, declared their intention to stick with the traditional kc. Mc. etc. units, sound is a traveling longitudinal wave which is an oscillation of pressure. Humans perceive frequency of waves as pitch. Each musical note corresponds to a frequency which can be measured in hertz. An infants ear is able to perceive frequencies ranging from 20 Hz to 20,000 Hz, the range of ultrasound, infrasound and other physical vibrations such as molecular and atomic vibrations extends from a few femtoHz into the terahertz range and beyond. Electromagnetic radiation is described by its frequency—the number of oscillations of the perpendicular electric and magnetic fields per second—expressed in hertz. Radio frequency radiation is measured in kilohertz, megahertz, or gigahertz

Hertz
–
Details of a

heartbeat as an example of a non-

sinusoidal periodic phenomenon that can be described in terms of hertz. Two complete cycles are illustrated.

Hertz
–
A

sine wave with varying frequency

18.
Joule
–
The joule, symbol J, is a derived unit of energy in the International System of Units. It is equal to the transferred to an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre. It is also the energy dissipated as heat when a current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule, one joule can also be defined as, The work required to move an electric charge of one coulomb through an electrical potential difference of one volt, or one coulomb volt. This relationship can be used to define the volt, the work required to produce one watt of power for one second, or one watt second. This relationship can be used to define the watt and this SI unit is named after James Prescott Joule. As with every International System of Units unit named for a person, note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, section 5.2. The CGPM has given the unit of energy the name Joule, the use of newton metres for torque and joules for energy is helpful to avoid misunderstandings and miscommunications. The distinction may be also in the fact that energy is a scalar – the dot product of a vector force. By contrast, torque is a vector – the cross product of a distance vector, torque and energy are related to one another by the equation E = τ θ, where E is energy, τ is torque, and θ is the angle swept. Since radians are dimensionless, it follows that torque and energy have the same dimensions, one joule in everyday life represents approximately, The energy required to lift a medium-size tomato 1 m vertically from the surface of the Earth. The energy released when that same tomato falls back down to the ground, the energy required to accelerate a 1 kg mass at 1 m·s−2 through a 1 m distance in space. The heat required to raise the temperature of 1 g of water by 0.24 °C, the typical energy released as heat by a person at rest every 1/60 s. The kinetic energy of a 50 kg human moving very slowly, the kinetic energy of a 56 g tennis ball moving at 6 m/s. The kinetic energy of an object with mass 1 kg moving at √2 ≈1.4 m/s, the amount of electricity required to light a 1 W LED for 1 s. Since the joule is also a watt-second and the unit for electricity sales to homes is the kW·h. For additional examples, see, Orders of magnitude The zeptojoule is equal to one sextillionth of one joule,160 zeptojoules is equivalent to one electronvolt. The nanojoule is equal to one billionth of one joule, one nanojoule is about 1/160 of the kinetic energy of a flying mosquito

Joule
–

Base units
19.
Katal
–
The katal is the SI unit of catalytic activity. It is a derived SI unit for quantifying the catalytic activity of enzymes and its use is recommended by the General Conference on Weights and Measures and other international organizations. It replaces the non-SI enzyme unit, enzyme units are, however, still more commonly used than the katal in practice at present, especially in biochemistry. The katal is not used to express the rate of a reaction, rather, it is used to express catalytic activity which is a property of the catalyst. The katal is invariant of the measurement procedure, but the quantity value is not. Therefore, in order to define the quantity of a catalyst, one katal of trypsin, for example, is that amount of trypsin which breaks a mole of peptide bonds per second under specified conditions. Kat = mol s The name katal has been used for decades, the name comes from the Ancient Greek κατάλυσις, meaning dissolution, which is the same origin as the word catalysis itself comes from. Unit katal for catalytic activity Pure Appl, the Tortuous Road to the Adoption of katal for the Expression of Catalytic Activity by the General Conference on Weights and Measures

Katal
–

Base units
20.
Lumen (unit)
–
The lumen is the SI derived unit of luminous flux, a measure of the total quantity of visible light emitted by a source. Lumens are related to lux in that one lux is one lumen per square meter, the lumen is defined in relation to the candela as 1 lm =1 cd ⋅ sr. A full sphere has an angle of 4π steradians, so a light source that uniformly radiates one candela in all directions has a total luminous flux of 1 cd × 4π sr = 4π cd⋅sr ≈12.57 lumens. If a light source emits one candela of luminous intensity uniformly across a solid angle of one steradian, alternatively, an isotropic one-candela light-source emits a total luminous flux of exactly 4π lumens. If the source were partly covered by an ideal absorbing hemisphere, the luminous intensity would still be one candela in those directions that are not obscured. The lumen can be thought of casually as a measure of the amount of visible light in some defined beam or angle. The number of candelas or lumens from a source also depends on its spectrum, the difference between the units lumen and lux is that the lux takes into account the area over which the luminous flux is spread. A flux of 1000 lumens, concentrated into an area of one square metre, the same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux. Mathematically,1 lx =1 lm/m2, a source radiating a power of one watt of light in the color for which the eye is most efficient has luminous flux of 683 lumens. So a lumen represents at least 1/683 watts of light power. Lamps used for lighting are commonly labelled with their output in lumens. A23 W spiral compact fluorescent lamp emits about 1, 400–1,600 lm, many compact fluorescent lamps and other alternative light sources are labelled as being equivalent to an incandescent bulb with a specific wattage. Below is a table that shows typical luminous flux for common incandescent bulbs, on September 1,2010, European Union legislation came into force mandating that lighting equipment must be labelled primarily in terms of luminous flux, instead of electric power. This change is a result of the EUs Eco-design Directive for Energy-using Products, for example, according to the European Union standard, an energy-efficient bulb that claims to be the equivalent of a 60 W tungsten bulb must have a minimum light output of 700–750 lm. The light output of projectors is typically measured in lumens, a standardized procedure for testing projectors has been established by the American National Standards Institute, which involves averaging together several measurements taken at different positions. For marketing purposes, the flux of projectors that have been tested according to this procedure may be quoted in ANSI lumens. ANSI lumen measurements are in more accurate than the other measurement techniques used in the projector industry. This allows projectors to be easily compared on the basis of their brightness specifications

Lumen (unit)
–

Base units
21.
Lux
–
The lux is the SI unit of illuminance and luminous emittance, measuring luminous flux per unit area. It is equal to one lumen per square metre, in photometry, this is used as a measure of the intensity, as perceived by the human eye, of light that hits or passes through a surface. In English, lux is used as both the singular and plural form, illuminance is a measure of how much luminous flux is spread over a given area. One can think of flux as a measure of the total amount of visible light present. A given amount of light will illuminate a surface more dimly if it is spread over a larger area, however, the same 1000 lumens, spread out over ten square metres, produces a dimmer illuminance of only 100 lux. Achieving an illuminance of 500 lux might be possible in a kitchen with a single fluorescent light fixture with an output of 12000 lumens. To light a factory floor with dozens of times the area of the kitchen would require dozens of such fixtures, thus, lighting a larger area to the same level of lux requires a greater number of lumens. As with other SI units, SI prefixes can be used, for instance, a star of apparent magnitude 0 provides 2.08 microlux at the earths surface. A barely perceptible magnitude 6 star provides 8 nanolux, the unobscured sun provides an illumination of up to 100 kilolux on the Earths surface, the exact value depending on time of year and atmospheric conditions. This direct normal illuminance is related to the solar illuminance constant Esc, the illumination provided on a surface by a point source equals the number of lux just described times the cosine of the angle between a ray coming from the source and a normal to the surface. The number of lux falling on the surface equals this cosine times a number that characterizes the source from the point of view in question and it differs from the luminance, which does depend on the angular distribution of the emission. A perfectly white surface with one lux falling on it will emit one lux, like all photometric units, the lux has a corresponding radiometric unit. The weighting factor is known as the luminosity function, the lux is one lumen per square metre, and the corresponding radiometric unit, which measures irradiance, is the watt per square metre. The peak of the luminosity function is at 555 nm, the eyes image-forming visual system is sensitive to light of this wavelength than any other. Other wavelengths of visible light produce fewer lux per watt-per-meter-squared, the luminosity function falls to zero for wavelengths outside the visible spectrum. For a light source with mixed wavelengths, the number of lumens per watt can be calculated by means of the luminosity function and this means that white light sources produce far fewer lumens per watt than the theoretical maximum of 683.002 lm/W. The ratio between the number of lumens per watt and the theoretical maximum is expressed as a percentage known as the luminous efficiency. For example, an incandescent light bulb has a luminous efficiency of only about 2%

Lux
–
A lux meter for measuring illuminances in work places.

22.
Newton (unit)
–
The newton is the International System of Units derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, see below for the conversion factors. One newton is the force needed to one kilogram of mass at the rate of one metre per second squared in direction of the applied force. In 1948, the 9th CGPM resolution 7 adopted the name newton for this force, the MKS system then became the blueprint for todays SI system of units. The newton thus became the unit of force in le Système International dUnités. This SI unit is named after Isaac Newton, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, section 5.2. Newtons second law of motion states that F = ma, where F is the applied, m is the mass of the object receiving the force. The newton is therefore, where the symbols are used for the units, N for newton, kg for kilogram, m for metre. In dimensional analysis, F = M L T2 where F is force, M is mass, L is length, at average gravity on earth, a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force, which we measure as the apples weight, for example, the tractive effort of a Class Y steam train and the thrust of an F100 fighter jet engine are both around 130 kN. One kilonewton,1 kN, is 102.0 kgf,1 kN =102 kg ×9.81 m/s2 So for example, a platform rated at 321 kilonewtons will safely support a 32,100 kilograms load. Specifications in kilonewtons are common in safety specifications for, the values of fasteners, Earth anchors. Working loads in tension and in shear, thrust of rocket engines and launch vehicles clamping forces of the various moulds in injection moulding machines used to manufacture plastic parts

Newton (unit)
–

Base units
23.
Pascal (unit)
–
The pascal is the SI derived unit of pressure used to quantify internal pressure, stress, Youngs modulus and ultimate tensile strength. It is defined as one newton per square meter and it is named after the French polymath Blaise Pascal. Common multiple units of the pascal are the hectopascal which is equal to one millibar, the unit of measurement called standard atmosphere is defined as 101,325 Pa and approximates to the average pressure at sea-level at the latitude 45° N. Meteorological reports typically state atmospheric pressure in hectopascals, the unit is named after Blaise Pascal, noted for his contributions to hydrodynamics and hydrostatics, and experiments with a barometer. The name pascal was adopted for the SI unit newton per square metre by the 14th General Conference on Weights, one pascal is the pressure exerted by a force of magnitude one newton perpendicularly upon an area of one square metre. The unit of measurement called atmosphere or standard atmosphere is 101325 Pa and this value is often used as a reference pressure and specified as such in some national and international standards, such as ISO2787, ISO2533 and ISO5024. In contrast, IUPAC recommends the use of 100 kPa as a standard pressure when reporting the properties of substances, geophysicists use the gigapascal in measuring or calculating tectonic stresses and pressures within the Earth. Medical elastography measures tissue stiffness non-invasively with ultrasound or magnetic resonance imaging, in materials science and engineering, the pascal measures the stiffness, tensile strength and compressive strength of materials. In engineering use, because the pascal represents a small quantity. The pascal is also equivalent to the SI unit of energy density and this applies not only to the thermodynamics of pressurised gases, but also to the energy density of electric, magnetic, and gravitational fields. In measurements of sound pressure, or loudness of sound, one pascal is equal to 94 decibels SPL, the quietest sound a human can hear, known as the threshold of hearing, is 0 dB SPL, or 20 µPa. The airtightness of buildings is measured at 50 Pa, the units of atmospheric pressure commonly used in meteorology were formerly the bar, which was close to the average air pressure on Earth, and the millibar. Since the introduction of SI units, meteorologists generally measure pressures in hectopascals unit, exceptions include Canada and Portugal, which use kilopascals. In many other fields of science, the SI is preferred, many countries also use the millibar or hectopascal to give aviation altimeter settings. In practically all fields, the kilopascal is used instead. Centimetre of water Metric prefix Orders of magnitude Pascals law

Pascal (unit)
–
A

pressure gauge reading in

psi (red scale) and kPa (black scale)

24.
Radian
–
The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a circle is numerically equal to the measurement in radians of the angle that it subtends. The unit was formerly an SI supplementary unit, but this category was abolished in 1995, separately, the SI unit of solid angle measurement is the steradian. The radian is represented by the symbol rad, so for example, a value of 1.2 radians could be written as 1.2 rad,1.2 r,1. 2rad, or 1. 2c. Radian describes the angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. Conversely, the length of the arc is equal to the radius multiplied by the magnitude of the angle in radians. As the ratio of two lengths, the radian is a number that needs no unit symbol, and in mathematical writing the symbol rad is almost always omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and it follows that the magnitude in radians of one complete revolution is the length of the entire circumference divided by the radius, or 2πr / r, or 2π. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees, the concept of radian measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He described the radian in everything but name, and he recognized its naturalness as a unit of angular measure, the idea of measuring angles by the length of the arc was already in use by other mathematicians. For example, al-Kashi used so-called diameter parts as units where one part was 1/60 radian. The term radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queens College, Belfast. He had used the term as early as 1871, while in 1869, Thomas Muir, then of the University of St Andrews, in 1874, after a consultation with James Thomson, Muir adopted radian. As stated, one radian is equal to 180/π degrees, thus, to convert from radians to degrees, multiply by 180/π. The length of circumference of a circle is given by 2 π r, so, to convert from radians to gradians multiply by 200 / π, and to convert from gradians to radians multiply by π /200. This is because radians have a mathematical naturalness that leads to a more elegant formulation of a number of important results, most notably, results in analysis involving trigonometric functions are simple and elegant when the functions arguments are expressed in radians. Because of these and other properties, the trigonometric functions appear in solutions to problems that are not obviously related to the functions geometrical meanings

Radian
–
A chart to convert between degrees and radians

Radian
–
An arc of a

circle with the same length as the

radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to an angle of 2

π radians.

25.
Siemens (unit)
–
The siemens is the unit of electric conductance, electric susceptance and electric admittance in the International System of Units. The 14th General Conference on Weights and Measures approved the addition of the siemens as a unit in 1971. The unit is named after Ernst Werner von Siemens, as with every SI unit whose name is derived from the proper name of a person, the first letter of its symbol is upper case, the lower-case s is the symbol for the second. When an SI unit is spelled out in English, it should begin with a lower-case letter. In English, the same form siemens is used both for the singular and plural, the unit siemens for the conductance G is defined by S = Ω −1 = A V where Ω is the ohm, A is the ampere, and V is the volt. For a device with a conductance of one siemens, the current through the device will increase by one ampere for every increase of one volt of electric potential difference across the device. The conductance of a resistor with a resistance of five ohms, for example, is −1, mho /moʊ/ is an alternative name of the same unit, the reciprocal of one ohm. Mho is derived from spelling ohm backwards and is written with an upside-down capital Greek letter Omega, ℧, according to Maver the term mho was suggested by Sir William Thomson. The mho was officially renamed to the siemens, replacing the old meaning of the siemens unit, the term siemens, as it is an SI term, is used universally in science and often in electrical applications, while mho is still used primarily in electronic applications. Likewise, it is difficult to distinguish the symbol S from the lower-case s where second is meant, brochure The International System of Units issued by the BIPM Different units named after Siemens

Siemens (unit)
–

Base units
26.
Sievert
–
The sievert, named after Rolf Maximilian Sievert, is a derived unit of ionizing radiation dose in the International System of Units. It is a measure of the effect of low levels of ionizing radiation on the human body. These are under review, and changes are advised in the formal Reports of those bodies. The sievert is used for radiation dose quantities such as equivalent dose, effective dose and it is used to represent both the risk of the effect of external radiation from sources outside the body and the effect of internal irradiation due to inhaled or ingested radioactive substances. Conventionally, the sievert is not used for high rates of radiation that produce deterministic effects. Such effects are compared to the physical quantity absorbed dose measured by the unit gray, one sievert carries with it a 5. 5% chance of eventually developing cancer based on the linear no-threshold model. The rem is an older, non-SI unit of measurement, in summary, The gray - quantity D1 Gy =1 joule/kilogram - a physical quantity. 1 Gy is the deposit of a joule of energy in a kg of matter or tissue. The sievert - quantity H1 Sv =1 joule/kilogram - a biological effect, the sievert represents the equivalent biological effect of the deposit of a joule of radiation energy in a kilogram of human tissue. The equivalence to absorbed dose is denoted by Q, the ICRP definition of the sievert is, The sievert is the special name for the SI unit of equivalent dose, effective dose, and operational dose quantities. The unit is joule per kilogram, the sievert is used for a number of dose quantities which are described in this article and are part of the international radiological protection system devised and defined by the ICRP and ICRU. The ICRU/ICRP dose quantities have specific purposes and meanings, but some use common words in a different order, there can be confusion between, for instance, equivalent dose and dose equivalent. Only the operational dose quantities which still use Q for calculation retain the phrase dose equivalent, however, there are joint ICRU/ICRP proposals to simplify this system by changes to the operational dose definitions to harmonise with those of protection quantities. In the USA there are differently named dose quantities which are not part of the ICRP nomenclature, the sievert is used to represent the biological effects of different forms of external ionizing radiation on various types of human tissue. Some quantities cannot be measured, but they must be related to actual instrumentation. The resultant complexity has required the creation of a number of different dose quantities within a coherent system developed by the ICRU working with the ICRP, the external dose quantities and their relationships are shown in the accompanying diagram. These are directly measurable physical quantities in which no allowance has been made for biological effects and these quantities cannot be practically measured but are a calculated value of dose of organs of the human body, which is arrived at by using anthropomorphic phantoms. These are 3D computational models of the body which take into account a number of complex effects such as body self-shielding

Sievert
–
External radiation dose quantities used in radiological protection

27.
Steradian
–
The steradian or square radian is the SI unit of solid angle. It is used in geometry, and is analogous to the radian which quantifies planar angles. The name is derived from the Greek stereos for solid and the Latin radius for ray and it is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol sr is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian, the steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit. A steradian can be defined as the angle subtended at the center of a unit sphere by a unit area on its surface. For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian, because the surface area A of a sphere is 4πr2, the definition implies that a sphere measures 4π steradians. By the same argument, the solid angle that can be subtended at any point is 4π sr. Since A = r2, it corresponds to the area of a cap. Therefore one steradian corresponds to the angle of the cross-section of a simple cone subtending the plane angle 2θ, with θ given by, θ = arccos = arccos = arccos ≈0.572 rad. This angle corresponds to the plane angle of 2θ ≈1.144 rad or 65. 54°. A steradian is also equal to the area of a polygon having an angle excess of 1 radian, to 1/4π of a complete sphere. The solid angle of a cone whose cross-section subtends the angle 2θ is, Ω =2 π s r. In two dimensions, an angle is related to the length of the arc that it spans, θ = l r r a d where l is arc length, r is the radius of the circle. For example, a measurement of the width of an object would be given in radians. At the same time its visible area over ones visible field would be given in steradians. Just as the area of a circle is related to its diameter or radius. One-dimensional circular measure has units of radians or degrees, while two-dimensional spherical measure is expressed in steradians, in higher dimensional mathematical spaces, units for analogous solid angles have not been explicitly named. When they are used, they are dealt with by analogy with the circular or spherical cases and that is, as a proportion of the relevant unit hypersphere taken up by the generalized angle, or point set expressed in spherical coordinates

Steradian
–
A graphical representation of 1 steradian. The sphere has radius r, and in this case the area A of the highlighted surface patch is r 2. The solid angle Ω equals A sr/ r 2 which is 1 sr in this example. The entire sphere has a solid angle of 4π sr.

28.
Tesla (unit)
–
The tesla is a unit of measurement of the strength of a magnetic field. It is a unit of the International System of Units. One tesla is equal to one weber per square metre, the unit was announced during the General Conference on Weights and Measures in 1960 and is named in honour of Nikola Tesla, upon the proposal of the Slovenian electrical engineer France Avčin. The strongest fields encountered from permanent magnets are from Halbach spheres, the strongest field trapped in a laboratory superconductor as of June 2014 is 21 T. This may be appreciated by looking at the units for each, the unit of electric field in the MKS system of units is newtons per coulomb, N/C, while the magnetic field can be written as N/. The dividing factor between the two types of field is metres per second, which is velocity, in ferromagnets, the movement creating the magnetic field is the electron spin. In a current-carrying wire the movement is due to moving through the wire. One tesla is equivalent to,10,000 G, used in the CGS system, thus,10 kG =1 T, and 1 G = 10−4 T.1,000,000,000 γ, used in geophysics. Thus,1 γ =1 nT.42.6 MHz of the 1H nucleus frequency, thus, the magnetic field associated with NMR at 1 GHz is 23.5 T. One tesla is equal to 1 V·s/m2 and this can be shown by starting with the speed of light in vacuum, c = −1/2, and inserting the SI values and units for c, the vacuum permittivity ε0, and the vacuum permeability μ0. Cancellation of numbers and units then produces this relation, for those concerned with low-frequency electromagnetic radiation in the home, the following conversions are needed most,1000 nT =1 µT =10 mG,1,000,000 µT =1 T. For the relation to the units of the field, see the article on permeability

Tesla (unit)
–
The tesla definition T = Wb / m 2 is prominently depicted on the 100

Serbian dinars banknote, along with the picture of

Nikola Tesla.

Tesla (unit)
–

Base units
29.
Volt
–
The volt is the derived unit for electric potential, electric potential difference, and electromotive force. One volt is defined as the difference in potential between two points of a conducting wire when an electric current of one ampere dissipates one watt of power between those points. It is also equal to the difference between two parallel, infinite planes spaced 1 meter apart that create an electric field of 1 newton per coulomb. Additionally, it is the difference between two points that will impart one joule of energy per coulomb of charge that passes through it. It can also be expressed as amperes times ohms, watts per ampere, or joules per coulomb, for the Josephson constant, KJ = 2e/h, the conventional value KJ-90 is used, K J-90 =0.4835979 GHz μ V. This standard is typically realized using an array of several thousand or tens of thousands of junctions. Empirically, several experiments have shown that the method is independent of device design, material, measurement setup, etc. in the water-flow analogy sometimes used to explain electric circuits by comparing them with water-filled pipes, voltage is likened to difference in water pressure. Current is proportional to the diameter of the pipe or the amount of water flowing at that pressure. A resistor would be a reduced diameter somewhere in the piping, the relationship between voltage and current is defined by Ohms Law. Ohms Law is analogous to the Hagen–Poiseuille equation, as both are linear models relating flux and potential in their respective systems, the voltage produced by each electrochemical cell in a battery is determined by the chemistry of that cell. Cells can be combined in series for multiples of that voltage, mechanical generators can usually be constructed to any voltage in a range of feasibility. High-voltage electric power lines,110 kV and up Lightning, Varies greatly. Volta had determined that the most effective pair of metals to produce electricity was zinc. In 1861, Latimer Clark and Sir Charles Bright coined the name volt for the unit of resistance, by 1873, the British Association for the Advancement of Science had defined the volt, ohm, and farad. In 1881, the International Electrical Congress, now the International Electrotechnical Commission and they made the volt equal to 108 cgs units of voltage, the cgs system at the time being the customary system of units in science. At that time, the volt was defined as the difference across a conductor when a current of one ampere dissipates one watt of power. The international volt was defined in 1893 as 1/1.434 of the emf of a Clark cell and this definition was abandoned in 1908 in favor of a definition based on the international ohm and international ampere until the entire set of reproducible units was abandoned in 1948. Prior to the development of the Josephson junction voltage standard, the volt was maintained in laboratories using specially constructed batteries called standard cells

Volt
–

Josephson junction array chip developed by the

National Bureau of Standards as a standard volt

Volt
–
A

multimeter can be used to measure the voltage between two positions.

Volt
–
1.5 V C-cell batteries

Volt
–
Alessandro Volta

30.
Weber (unit)
–
In physics, the weber /ˈweɪbər/ is the SI unit of magnetic flux. A flux density of one Wb/m2 is one tesla, the weber is named after the German physicist Wilhelm Eduard Weber. The weber may be defined in terms of Faradays law, which relates a changing magnetic flux through a loop to the field around the loop. A change in flux of one weber per second will induce an electromotive force of one volt. Officially, Weber — The weber is the flux that, linking a circuit of one turn. This SI unit is named after Wilhelm Eduard Weber, as with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that degree Celsius conforms to this rule because the d is lowercase. — Based on The International System of Units, in 1861, the British Association for the Advancement of Science established a committee under William Thomson to study electrical units. It was not until 1927 that TC1 dealt with the study of various outstanding problems concerning electrical and magnetic quantities, as disagreement continued, the IEC decided on an effort to remedy the situation. It instructed a task force to study the question in readiness for the next meeting, in 1935, TC1 recommended names for several electrical units, including the weber for the practical unit of magnetic flux. This system was given the designation of Giorgi system, also in 1936, TC1 passed responsibility for electric and magnetic magnitudes and units to the new TC24. This led eventually to the adoption of the Giorgi system, which unified electromagnetic units with the MKS dimensional system of units. In 1938, TC24 recommended as a link the permeability of free space with the value of µ0 = 4π×10−7 H/m. This group also recognized that any one of the units already in use. After consultation, the ampere was adopted as the unit of the Giorgi system in Paris in 1950

Weber (unit)
–

Base units
31.
Astronomical unit
–
The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that varies as Earth orbits the Sun, from a maximum to a minimum. Originally conceived as the average of Earths aphelion and perihelion, it is now defined as exactly 149597870700 metres, the astronomical unit is used primarily as a convenient yardstick for measuring distances within the Solar System or around other stars. However, it is also a component in the definition of another unit of astronomical length. A variety of symbols and abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the symbol A for the astronomical unit, in 2006, the International Bureau of Weights and Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting that various symbols are presently in use for the astronomical unit, in the 2014 revision of the SI Brochure, the BIPM used the unit symbol au. In ISO 80000-3, the symbol of the unit is ua. Earths orbit around the Sun is an ellipse, the semi-major axis of this ellipse is defined to be half of the straight line segment that joins the aphelion and perihelion. The centre of the sun lies on this line segment. In addition, it mapped out exactly the largest straight-line distance that Earth traverses over the course of a year, knowing Earths shift and a stars shift enabled the stars distance to be calculated. But all measurements are subject to some degree of error or uncertainty, improvements in precision have always been a key to improving astronomical understanding. Improving measurements were continually checked and cross-checked by means of our understanding of the laws of celestial mechanics, the expected positions and distances of objects at an established time are calculated from these laws, and assembled into a collection of data called an ephemeris. NASAs Jet Propulsion Laboratory provides one of several ephemeris computation services, in 1976, in order to establish a yet more precise measure for the astronomical unit, the IAU formally adopted a new definition. Equivalently, by definition, one AU is the radius of an unperturbed circular Newtonian orbit about the sun of a particle having infinitesimal mass. As with all measurements, these rely on measuring the time taken for photons to be reflected from an object. However, for precision the calculations require adjustment for such as the motions of the probe. In addition, the measurement of the time itself must be translated to a scale that accounts for relativistic time dilation

Astronomical unit
–
Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called "

black drop effect ") and the rarity of observations.

Astronomical unit
–
The red line indicates the Earth-Sun distance, which is on average about 1 astronomical unit.

32.
Bar (unit)
–
The bar is a metric unit of pressure, but is not approved as part of the International System of Units. It is defined as equal to 100000 Pa, which is slightly less than the current average atmospheric pressure on Earth at sea level. The bar and the millibar were introduced by the Norwegian meteorologist Vilhelm Bjerknes, use of the bar is deprecated by some professional bodies in some fields. The International Astronomical Union also lists it under Non-SI units and symbols whose continued use is deprecated, as of 2004, the bar is legally recognized in countries of the European Union. Units derived from the bar include the megabar, kilobar, decibar, centibar, the notation bar, though deprecated by various bodies, represents gauge pressure, i. e. pressure in bars above ambient or atmospheric pressure. The bar is defined using the SI derived unit, pascal,1 bar ≡100000 Pa. Thus,1 bar is equal to,100 kPa 1×105 N/m21000000 Ba, notes,1 millibar =1 one-thousandth bar, or 1×10−3 bar 1 millibar =1 hectopascal. The word bar has its origin in the Greek word βάρος, the units official symbol is bar, the earlier symbol b is now deprecated and conflicts with the use of b denoting the unit barn, but it is still encountered, especially as mb to denote the millibar. Between 1793 and 1795, the bar was used for a unit of weight in an early version of the metric system. Atmospheric air pressure is given in millibars where standard sea level pressure is defined as 1013 mbar,101.3,1.013 bar. Despite the millibar not being an SI unit, meteorologists and weather reporters worldwide have long measured air pressure in millibars as the values are convenient, for example, the weather office of Environment Canada uses kilopascals and hectopascals on their weather maps. In contrast, Americans are familiar with the use of the millibar in US reports of hurricanes, in fresh water, there is an approximate numerical equivalence between the change in pressure in decibars and the change in depth from the water surface in metres. Specifically, an increase of 1 decibar occurs for every 1.019716 m increase in depth, in sea water with respect to the gravity variation, the latitude and the geopotential anomaly the pressure can be converted into meters depth according to an empirical formula. As a result, decibars are commonly used in oceanography, many engineers worldwide use the bar as a unit of pressure because, in much of their work, using pascals would involve using very large numbers. In the automotive field, turbocharger boost is often described in bars outside the USA), unicode has characters for mb and bar, but they exist only for compatibility with legacy Asian encodings and are not intended to be used in new documents. The kilobar, equivalent to 100 MPa, is used in geological systems. Bar and bara are sometimes used to indicate absolute pressures and bar and this usage is deprecated and fuller descriptions such as gauge pressure of 2 bar or 2 bar gauge are recommended.0 Unported License but not under the GFDL. Non-SI units accepted for use with the SI

Bar (unit)
–
An aluminium cylinder (5 mm or 0.197 in thickness) after 700 bar (10 ksi) pressure.

33.
Atomic mass unit
–
The unified atomic mass unit or dalton is a standard unit of mass that quantifies mass on an atomic or molecular scale. One unified atomic mass unit is approximately the mass of one nucleon and is equivalent to 1 g/mol. The CIPM has categorised it as a non-SI unit accepted for use with the SI, the amu without the unified prefix is technically an obsolete unit based on oxygen, which was replaced in 1961. However, many still use the term amu but now define it in the same way as u. In this sense, most uses of the atomic mass units. For standardization a specific atomic nucleus had to be chosen because the mass of a nucleon depends on the count of the nucleons in the atomic nucleus due to mass defect. This is also why the mass of a proton or neutron by itself is more than 1 u, the atomic mass unit is not the unit of mass in the atomic units system, which is rather the electron rest mass. The relative atomic mass scale has traditionally been a relative value and this evaluation was made prior to the discovery of the existence of elemental isotopes, which occurred in 1912. The divergence of these values could result in errors in computations, the chemistry amu, based on the relative atomic mass of natural oxygen, was about 1.000282 as massive as the physics amu, based on pure isotopic 16O. For these and other reasons, the standard for both physics and chemistry was changed to carbon-12 in 1961. The choice of carbon-12 was made to minimise further divergence with prior literature. The new and current unit was referred to as the atomic mass unit u. and given a new symbol, u. The Dalton is another name for the atomic mass unit. 1 u = m u =112 m Despite this change, modern sources often use the old term amu but define it as u. Therefore, in general, amu likely does not refer to the old oxygen standard unit, the unified atomic mass unit and the dalton are different names for the same unit of measure. As with other names such as watt and newton, dalton is not capitalized in English. In 2003 the Consultative Committee for Units, part of the CIPM, recommended a preference for the usage of the dalton over the atomic mass unit as it is shorter. In 2005, the International Union of Pure and Applied Physics endorsed the use of the dalton as an alternative to the atomic mass unit

Atomic mass unit
–

Base units
34.
Day
–
In common usage, it is either an interval equal to 24 hours or daytime, the consecutive period of time during which the Sun is above the horizon. The period of time during which the Earth completes one rotation with respect to the Sun is called a solar day, several definitions of this universal human concept are used according to context, need and convenience. In 1960, the second was redefined in terms of the motion of the Earth. The unit of measurement day, redefined in 1960 as 86400 SI seconds and symbolized d, is not an SI unit, but is accepted for use with SI. The word day may also refer to a day of the week or to a date, as in answer to the question. The life patterns of humans and many species are related to Earths solar day. In recent decades the average length of a day on Earth has been about 86400.002 seconds. A day, understood as the span of time it takes for the Earth to make one rotation with respect to the celestial background or a distant star, is called a stellar day. This period of rotation is about 4 minutes less than 24 hours, mainly due to tidal effects, the Earths rotational period is not constant, resulting in further minor variations for both solar days and stellar days. Other planets and moons have stellar and solar days of different lengths to Earths, besides the day of 24 hours, the word day is used for several different spans of time based on the rotation of the Earth around its axis. An important one is the day, defined as the time it takes for the Sun to return to its culmination point. Because the Earth orbits the Sun elliptically as the Earth spins on an inclined axis, on average over the year this day is equivalent to 24 hours. A day, in the sense of daytime that is distinguished from night-time, is defined as the period during which sunlight directly reaches the ground. The length of daytime averages slightly more than half of the 24-hour day, two effects make daytime on average longer than nights. The Sun is not a point, but has an apparent size of about 32 minutes of arc, additionally, the atmosphere refracts sunlight in such a way that some of it reaches the ground even when the Sun is below the horizon by about 34 minutes of arc. So the first light reaches the ground when the centre of the Sun is still below the horizon by about 50 minutes of arc, the difference in time depends on the angle at which the Sun rises and sets, but can amount to around seven minutes. Ancient custom has a new day start at either the rising or setting of the Sun on the local horizon, the exact moment of, and the interval between, two sunrises or sunsets depends on the geographical position, and the time of year. A more constant day can be defined by the Sun passing through the local meridian, the exact moment is dependent on the geographical longitude, and to a lesser extent on the time of the year

Day
–

Water,

Rabbit, and

Deer: three of the 20 day symbols in the

Aztec calendar, from the

Aztec calendar stone
Day
–

Dagr, the

Norse god of the day, rides his horse in this 19th-century painting by

Peter Nicolai Arbo.

Day
–

Sun and

Moon, Hartmann Schedel's

Nuremberg Chronicle, 1493

Day
–
Key concepts

35.
Decibel
–
The decibel is a logarithmic unit used to express the ratio of two values of a physical quantity. One of these values is often a reference value, in which case the decibel is used to express the level of the other value relative to this reference. When used in way, the decibel symbol is often qualified with a suffix that indicates the reference quantity that has been used or some other property of the quantity being measured. For example, dBm indicates a power of one milliwatt. There are two different scales used when expressing a ratio in decibels depending on the nature of the quantities, when expressing power quantities, the number of decibels is ten times the logarithm to base 10 of the ratio of two power quantities. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level, when expressing field quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The difference in scales relates to the square law of fields in three-dimensional linear space. The decibel scales differ so that comparisons can be made between related power and field quantities when they are expressed in decibels. The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell, however, today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics, electronics, and control theory. In electronics, the gains of amplifiers, attenuation of signals, the decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. The unit for loss was originally Miles of Standard Cable, the standard telephone cable implied was a cable having uniformly distributed resistance of 88 ohms per loop mile and uniformly distributed shunt capacitance of 0.054 microfarad per mile. 1 TU was defined such that the number of TUs was ten times the logarithm of the ratio of measured power to a reference power level. The definition was conveniently chosen such that 1 TU approximated 1 MSC, in 1928, the Bell system renamed the TU into the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio. It was named the bel, in honor of the telecommunications pioneer Alexander Graham Bell, the bel is seldom used, as the decibel was the proposed working unit. However, the decibel is recognized by international bodies such as the International Electrotechnical Commission. The term field quantity is deprecated by ISO 80000-1, which favors root-power, in spite of their widespread use, suffixes are not recognized by the IEC or ISO. The ISO Standard 80000-3,2006 defines the following quantities, the decibel is one-tenth of a bel,1 dB =0.1 B

Decibel
–

Base units
36.
Degree (angle)
–
A degree, usually denoted by °, is a measurement of a plane angle, defined so that a full rotation is 360 degrees. It is not an SI unit, as the SI unit of measure is the radian. Because a full rotation equals 2π radians, one degree is equivalent to π/180 radians, the original motivation for choosing the degree as a unit of rotations and angles is unknown. One theory states that it is related to the fact that 360 is approximately the number of days in a year. Ancient astronomers noticed that the sun, which follows through the path over the course of the year. Some ancient calendars, such as the Persian calendar, used 360 days for a year, the use of a calendar with 360 days may be related to the use of sexagesimal numbers. The earliest trigonometry, used by the Babylonian astronomers and their Greek successors, was based on chords of a circle, a chord of length equal to the radius made a natural base quantity. One sixtieth of this, using their standard sexagesimal divisions, was a degree, Aristarchus of Samos and Hipparchus seem to have been among the first Greek scientists to exploit Babylonian astronomical knowledge and techniques systematically. Timocharis, Aristarchus, Aristillus, Archimedes, and Hipparchus were the first Greeks known to divide the circle in 360 degrees of 60 arc minutes, eratosthenes used a simpler sexagesimal system dividing a circle into 60 parts. Furthermore, it is divisible by every number from 1 to 10 except 7 and this property has many useful applications, such as dividing the world into 24 time zones, each of which is nominally 15° of longitude, to correlate with the established 24-hour day convention. Finally, it may be the case more than one of these factors has come into play. For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates, degree measurements may be written using decimal degrees, with the symbol behind the decimals. Alternatively, the sexagesimal unit subdivisions can be used. One degree is divided into 60 minutes, and one minute into 60 seconds, use of degrees-minutes-seconds is also called DMS notation. These subdivisions, also called the arcminute and arcsecond, are represented by a single and double prime. For example,40. 1875° = 40° 11′ 15″, or, using quotation mark characters, additional precision can be provided using decimals for the arcseconds component. The older system of thirds, fourths, etc. which continues the sexagesimal unit subdivision, was used by al-Kashi and other ancient astronomers, but is rarely used today

Degree (angle)
–
One degree (shown in red) and eighty nine (shown in blue)

37.
Electronvolt
–
In physics, the electronvolt is a unit of energy equal to approximately 1. 6×10−19 joules. By definition, it is the amount of energy gained by the charge of an electron moving across an electric potential difference of one volt. Thus it is 1 volt multiplied by the elementary charge, therefore, one electronvolt is equal to 6981160217662079999♠1. 6021766208×10−19 J. The electronvolt is not a SI unit, and its definition is empirical, like the elementary charge on which it is based, it is not an independent quantity but is equal to 1 J/C √2hα / μ0c0. It is a unit of energy within physics, widely used in solid state, atomic, nuclear. It is commonly used with the metric prefixes milli-, kilo-, in some older documents, and in the name Bevatron, the symbol BeV is used, which stands for billion electronvolts, it is equivalent to the GeV. By mass–energy equivalence, the electronvolt is also a unit of mass and it is common in particle physics, where units of mass and energy are often interchanged, to express mass in units of eV/c2, where c is the speed of light in vacuum. It is common to express mass in terms of eV as a unit of mass. The mass equivalent of 1 eV/c2 is 1 eV / c 2 = ⋅1 V2 =1.783 ×10 −36 kg. For example, an electron and a positron, each with a mass of 0.511 MeV/c2, the proton has a mass of 0.938 GeV/c2. In general, the masses of all hadrons are of the order of 1 GeV/c2, the unified atomic mass unit,1 gram divided by Avogadros number, is almost the mass of a hydrogen atom, which is mostly the mass of the proton. To convert to megaelectronvolts, use the formula,1 u =931.4941 MeV/c2 =0.9314941 GeV/c2, in high-energy physics, the electronvolt is often used as a unit of momentum. A potential difference of 1 volt causes an electron to gain an amount of energy and this gives rise to usage of eV as units of momentum, for the energy supplied results in acceleration of the particle. The dimensions of units are LMT−1. The dimensions of units are L2MT−2. Then, dividing the units of energy by a constant that has units of velocity. In the field of particle physics, the fundamental velocity unit is the speed of light in vacuum c. Thus, dividing energy in eV by the speed of light, the fundamental velocity constant c is often dropped from the units of momentum by way of defining units of length such that the value of c is unity

Electronvolt
–
γ:

Gamma rays
38.
Hectare
–
The hectare is an SI accepted metric system unit of area equal to 100 ares and primarily used in the measurement of land as a metric replacement for the imperial acre. An acre is about 0.405 hectare and one hectare contains about 2.47 acres, in 1795, when the metric system was introduced, the are was defined as 100 square metres and the hectare was thus 100 ares or 1⁄100 km2. When the metric system was further rationalised in 1960, resulting in the International System of Units, the are was not included as a recognised unit. The hectare, however, remains as a non-SI unit accepted for use with the SI units, the metric system of measurement was first given a legal basis in 1795 by the French Revolutionary government. At the first meeting of the CGPM in 1889 when a new standard metre, manufactured by Johnson Matthey & Co of London was adopted, in 1960, when the metric system was updated as the International System of Units, the are did not receive international recognition. The units that were catalogued replicated the recommendations of the CGPM, many farmers, especially older ones, still use the acre for everyday calculations, and convert to hectares only for official paperwork. Farm fields can have long histories which are resistant to change, with names such as the six acre field stretching back hundreds of years. The names centiare, deciare, decare and hectare are derived by adding the standard metric prefixes to the base unit of area. The centiare is a synonym for one square metre, the deciare is ten square metres. The are is a unit of area, equal to 100 square metres and it was defined by older forms of the metric system, but is now outside of the modern International System of Units. It is commonly used to measure real estate, in particular in Indonesia, India, and in French-, Portuguese-, Slovakian-, Serbian-, Czech-, Polish-, Dutch-, in Russia and other former Soviet Union states, the are is called sotka. It is used to describe the size of suburban dacha or allotment garden plots or small city parks where the hectare would be too large, the decare is derived from deka, the prefix for 10 and are, and is equal to 10 ares or 1000 square metres. It is used in Norway and in the former Ottoman areas of the Middle East, the hectare, although not strictly a unit of SI, is the only named unit of area that is accepted for use within the SI. The United Kingdom, United States, Burma, and to some extent Canada instead use the acre, others, such as South Africa, published conversion factors which were to be used particularly when preparing consolidation diagrams by compilation. In many countries, metrication redefined or clarified existing measures in terms of metric units, non-SI units accepted for use with the International System of Units

Hectare
–

Trafalgar Square has an area of about one hectare.

Hectare
–
Definition of a hectare and of an are.

Hectare
–

Waikato Stadium – Hamilton, New Zealand

Hectare
–

The Statue of Liberty –

New York Harbor
39.
Hour
–
An hour is a unit of time conventionally reckoned as 1⁄24 of a day and scientifically reckoned as 3, 599–3,601 seconds, depending on conditions. The seasonal, temporal, or unequal hour was established in the ancient Near East as 1⁄12 of the night or daytime, such hours varied by season, latitude, and weather. It was subsequently divided into 60 minutes, each of 60 seconds, the modern English word hour is a development of the Anglo-Norman houre and Middle English ure, first attested in the 13th century. It displaced the Old English tide and stound, the Anglo-Norman term was a borrowing of Old French ure, a variant of ore, which derived from Latin hōra and Greek hṓrā. Like Old English tīd and stund, hṓrā was originally a word for any span of time, including seasons. Its Proto-Indo-European root has been reconstructed as *yeh₁-, making hour distantly cognate with year, the time of day is typically expressed in English in terms of hours. Whole hours on a 12-hour clock are expressed using the contracted phrase oclock, Hours on a 24-hour clock are expressed as hundred or hundred hours. Fifteen and thirty minutes past the hour is expressed as a quarter past or after and half past, respectively, fifteen minutes before the hour may be expressed as a quarter to, of, till, or before the hour. Sumerian and Babylonian hours divided the day and night into 24 equal hours, the ancient Egyptians began dividing the night into wnwt at some time before the compilation of the Dynasty V Pyramid Texts in the 24th century BC. By 2150 BC, diagrams of stars inside Egyptian coffin lids—variously known as diagonal calendars or star clocks—attest that there were exactly 12 of these. The coffin diagrams show that the Egyptians took note of the risings of 36 stars or constellations. Each night, the rising of eleven of these decans were noted, the original decans used by the Egyptians would have fallen noticeably out of their proper places over a span of several centuries. By the time of Amenhotep III, the priests at Karnak were using water clocks to determine the hours and these were filled to the brim at sunset and the hour determined by comparing the water level against one of its twelve gauges, one for each month of the year. During the New Kingdom, another system of decans was used, the later division of the day into 12 hours was accomplished by sundials marked with ten equal divisions. The morning and evening periods when the failed to note time were observed as the first and last hours. The Egyptian hours were closely connected both with the priesthood of the gods and with their divine services, by the New Kingdom, each hour was conceived as a specific region of the sky or underworld through which Ras solar bark travelled. Protective deities were assigned to each and were used as the names of the hours, as the protectors and resurrectors of the sun, the goddesses of the night hours were considered to hold power over all lifespans and thus became part of Egyptian funerary rituals. The Egyptian for astronomer, used as a synonym for priest, was wnwty, the earliest forms of wnwt include one or three stars, with the later solar hours including the determinative hieroglyph for sun

Hour
–
Key concepts

Hour
–
Midnight on a 24-hour digital clock

40.
Litre
–
The litre or liter is an SI accepted metric system unit of volume equal to 1 cubic decimetre,1,000 cubic centimetres or 1/1,000 cubic metre. A cubic decimetre occupies a volume of 10×10×10 centimetres and is equal to one-thousandth of a cubic metre. The original French metric system used the litre as a base unit. The word litre is derived from an older French unit, the litron, whose name came from Greek — where it was a unit of weight, not volume — via Latin, and which equalled approximately 0.831 litres. The litre was also used in subsequent versions of the metric system and is accepted for use with the SI. The spelling used by the International Bureau of Weights and Measures is litre, the less common spelling of liter is more predominantly used in American English. One litre of water has a mass of almost exactly one kilogram. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact, a litre is defined as a special name for a cubic decimetre or 10 centimetres ×10 centimetres ×10 centimetres. Hence 1 L ≡0.001 m3 ≡1000 cm3, from 1901 to 1964, the litre was defined as the volume of one kilogram of pure water at maximum density and standard pressure. The kilogram was in turn specified as the mass of a platinum/iridium cylinder held at Sèvres in France and was intended to be of the mass as the 1 litre of water referred to above. It was subsequently discovered that the cylinder was around 28 parts per million too large and thus, during this time, additionally, the mass-volume relationship of water depends on temperature, pressure, purity and isotopic uniformity. In 1964, the definition relating the litre to mass was abandoned in favour of the current one, although the litre is not an official SI unit, it is accepted by the CGPM for use with the SI. CGPM defines the litre and its acceptable symbols, a litre is equal in volume to the millistere, an obsolete non-SI metric unit customarily used for dry measure. The litre is often used in some calculated measurements, such as density. One litre of water has a mass of almost exactly one kilogram when measured at its maximal density, similarly,1 millilitre of water has a mass of about 1 g,1,000 litres of water has a mass of about 1,000 kg. It is now known that density of water depends on the isotopic ratios of the oxygen and hydrogen atoms in a particular sample. The litre, though not an official SI unit, may be used with SI prefixes, the most commonly used derived unit is the millilitre, defined as one-thousandth of a litre, and also often referred to by the SI derived unit name cubic centimetre. It is a commonly used measure, especially in medicine and cooking, Other units may be found in the table below, where the more often used terms are in bold

Litre
–

Maßkrüge (1-litre beer mugs) during the 2006

Oktoberfest in Germany

Litre
–
One litre is the volume of a cube with 10 cm sides

41.
Minute
–
The minute is a unit of time or of angle. As a unit of time, the minute is equal to 1⁄60 of an hour, in the UTC time standard, a minute on rare occasions has 61 seconds, a consequence of leap seconds. As a unit of angle, the minute of arc is equal to 1⁄60 of a degree, although not an SI unit for either time or angle, the minute is accepted for use with SI units for both. The SI symbols for minute or minutes are min for time measurement, the prime is also sometimes used informally to denote minutes of time. In contrast to the hour, the minute does not have a historical background. What is traceable only is that it started being recorded in the Middle Ages due to the ability of construction of precision timepieces, however, no consistent records of the origin for the division as 1⁄60 part of the hour have ever been found, despite many speculations. Historically, the word comes from the Latin pars minuta prima. This division of the hour can be refined with a second small part. For even further refinement, the third remains in some languages, for example Polish and Turkish. The symbol notation of the prime for minutes and double prime for seconds can be seen as indicating the first, international System of Units Latitude and longitude Orders of magnitude Henry Campbell Black, Blacks Law Dictionary, 6th Edition, entry on Minute. West Publishing Company, St. Paul, Minnesota,1991

Minute
–
Key concepts

Minute
–

Base units
42.
Minute and second of arc
–
A minute of arc, arcminute, arc minute, or minute arc is a unit of angular measurement equal to 1/60 of one degree. Since one degree is 1/360 of a turn, one minute of arc is 1/21600 of a turn, a second of arc, arcsecond, or arc second is 1/60 of an arcminute, 1/3600 of a degree, 1/1296000 of a turn, and π/648000 of a radian. To express even smaller angles, standard SI prefixes can be employed, the number of square arcminutes in a complete sphere is 4 π2 =466560000 π ≈148510660 square arcminutes. The standard symbol for marking the arcminute is the prime, though a single quote is used where only ASCII characters are permitted. One arcminute is thus written 1′ and it is also abbreviated as arcmin or amin or, less commonly, the prime with a circumflex over it. The standard symbol for the arcsecond is the prime, though a double quote is commonly used where only ASCII characters are permitted. One arcsecond is thus written 1″ and it is also abbreviated as arcsec or asec. In celestial navigation, seconds of arc are used in calculations. This notation has been carried over into marine GPS receivers, which normally display latitude and longitude in the format by default. An arcsecond is approximately the angle subtended by a U. S. dime coin at a distance of 4 kilometres, a milliarcsecond is about the size of a dime atop the Eiffel Tower as seen from New York City. A microarcsecond is about the size of a period at the end of a sentence in the Apollo mission manuals left on the Moon as seen from Earth, since antiquity the arcminute and arcsecond have been used in astronomy. The principal exception is Right ascension in equatorial coordinates, which is measured in units of hours, minutes. These small angles may also be written in milliarcseconds, or thousandths of an arcsecond, the unit of distance, the parsec, named from the parallax of one arcsecond, was developed for such parallax measurements. It is the distance at which the radius of the Earths orbit would subtend an angle of one arcsecond. The ESA astrometric space probe Gaia is hoped to measure star positions to 20 microarcseconds when it begins producing catalog positions sometime after 2016, there are about 1.3 trillion µas in a turn. Currently the best catalog positions of stars actually measured are in terms of milliarcseconds, apart from the Sun, the star with the largest angular diameter from Earth is R Doradus, a red supergiant with a diameter of 0.05 arcsecond. The dwarf planet Pluto has proven difficult to resolve because its angular diameter is about 0.1 arcsecond, space telescopes are not affected by the Earths atmosphere but are diffraction limited. For example, the Hubble space telescope can reach a size of stars down to about 0. 1″

Minute and second of arc
–
Comparison of angular diameter of the Sun, Moon, planets and the International Space Station. To get a true representation of the sizes, view the image at a distance of 103 times the width of the "Moon: max." circle. For example, if this circle is 10 cm wide on your monitor, view it from 10.3 m away.

43.
Neper
–
The neper is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The units name is derived from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit of the International System of Quantities, but not part of the International System of Units, like the decibel, the neper is a unit in a logarithmic scale. While the bel uses the logarithm to compute ratios, the neper uses the natural logarithm. The value of a ratio in nepers is given by L N p = ln x 1 x 2 = ln x 1 − ln x 2, where x 1 and x 2 are the values of interest, and ln is the natural logarithm. When the values are quadratic in the amplitude, they are first linearised by taking the square root before the logarithm is taken, in the ISQ, the neper is defined as 1 Np =1. The neper is defined in terms of ratios of field quantities, a power ratio 10 log r dB is equivalent to a field-quantity ratio 20 log r dB, since power is proportional to the square of the amplitude. Hence the neper and decibel are related via,1 N p =20 log 10 e d B ≈8,685889638 d B and 1 d B =120 log 10 e N p ≈0. The decibel and the neper have a ratio to each other. Like the decibel, the neper is a dimensionless unit, the International Telecommunication Union recognizes both units. The neper is a linear unit of relative difference, meaning in nepers, relative differences add. This property is shared with logarithmic units in other bases, such as the bel, the centineper can thus be used as a linear replacement for percentage differences. The linear approximation for small differences, =1 + δ + ϵ + δ ϵ ≈1 + δ + ϵ, is widely used. However, it is approximate, with error increasing for large percentage changes. Conversion of level gain and loss, neper, decibel, and bel Calculating transmission line losses

Neper
–

Base units
44.
Tonne
–
The SI symbol for the tonne is t, adopted at the same time as the unit itself in 1879. Its use is also official, for the metric ton, within the United States, having been adopted by the US National Institute of Standards and it is a symbol, not an abbreviation, and should not be followed by a period. Informal and non-approved symbols or abbreviations include T, mT, MT, in French and all English-speaking countries that are predominantly metric, tonne is the correct spelling. Before metrication in the UK the unit used for most purposes was the Imperial ton of 2,240 pounds avoirdupois, equivalent to 1,016 kg, differing by just 1. 6% from the tonne. Ton and tonne are both derived from a Germanic word in use in the North Sea area since the Middle Ages to designate a large cask. A full tun, standing about a high, could easily weigh a tonne. An English tun of wine weighs roughly a tonne,954 kg if full of water, in the United States, the unit was originally referred to using the French words millier or tonneau, but these terms are now obsolete. The Imperial and US customary units comparable to the tonne are both spelled ton in English, though they differ in mass, one tonne is equivalent to, Metric/SI,1 megagram. Equal to 1000000 grams or 1000 kilograms, megagram, Mg, is the official SI unit. Mg is distinct from mg, milligram, pounds, Exactly 1000/0. 453 592 37 lb, or approximately 2204.622622 lb. US/Short tons, Exactly 1/0. 907 184 74 short tons, or approximately 1.102311311 ST. One short ton is exactly 0.90718474 t, imperial/Long tons, Exactly 1/1. 016 046 9088 long tons, or approximately 0.9842065276 LT. One long ton is exactly 1.0160469088 t, for multiples of the tonne, it is more usual to speak of thousands or millions of tonnes. Kilotonne, megatonne, and gigatonne are more used for the energy of nuclear explosions and other events. When used in context, there is little need to distinguish between metric and other tons, and the unit is spelt either as ton or tonne with the relevant prefix attached. *The equivalent units columns use the short scale large-number naming system used in most English-language countries. †Values in the equivalent short and long tons columns are rounded to five significant figures, ǂThough non-standard, the symbol kt is also sometimes used for knot, a unit of speed for sea-going vessels, and should not be confused with kilotonne. A metric ton unit can mean 10 kilograms within metal trading and it traditionally referred to a metric ton of ore containing 1% of metal. In the case of uranium, the acronym MTU is sometimes considered to be metric ton of uranium, in the petroleum industry the tonne of oil equivalent is a unit of energy, the amount of energy released by burning one tonne of crude oil, approximately 42 GJ

Tonne
–

Base units
45.
Atomic units
–
Atomic units form a system of natural units which is especially convenient for atomic physics calculations. There are two different kinds of units, Hartree atomic units and Rydberg atomic units, which differ in the choice of the unit of mass. In Hartree units, the speed of light is approximately 137, atomic units are often abbreviated a. u. or au, not to be confused with the same abbreviation used also for astronomical units, arbitrary units, and absorbance units in different contexts. Atomic units, like SI units, have a unit of mass, a unit of length, however, the use and notation is somewhat different from SI. Suppose a particle with a mass of m has 3.4 times the mass of electron, the value of m can be written in three ways, m =3.4 m e. This is the clearest notation, where the unit is included explicitly as a symbol. This notation is ambiguous, Here, it means that the m is 3.4 times the atomic unit of mass. But if a length L were 3.4 times the unit of length. The dimension needs to be inferred from context and this notation is similar to the previous one, and has the same dimensional ambiguity. It comes from setting the atomic units to 1, in this case m e =1. These four fundamental constants form the basis of the atomic units, therefore, their numerical values in the atomic units are unity by definition. Dimensionless physical constants retain their values in any system of units, of particular importance is the fine-structure constant α = e 2 ℏ c ≈1 /137. This immediately gives the value of the speed of light, expressed in atomic units, below are given a few derived units. Some of them have names and symbols assigned, as indicated in the table. There are two variants of atomic units, one where they are used in conjunction with SI units for electromagnetism. Although the units written above are the same way, the units related to magnetism are not. In the SI system, the unit for magnetic field is 1 a. u. = ℏ e a 02 =2. 35×105 T =2. 35×109 G, and in the Gaussian-cgs unit system, = e a 02 c =1. 72×103 T =1. 72×107 G

Atomic units
–

Base units
46.
Natural units
–
In physics, natural units are physical units of measurement based only on universal physical constants. For example, the charge e is a natural unit of electric charge. It precludes the interpretation of an expression in terms of physical constants, such e and c. In this case, the reinsertion of the powers of e, c. Natural units are natural because the origin of their definition comes only from properties of nature, Planck units are often, without qualification, called natural units, although they constitute only one of several systems of natural units, albeit the best known such system. As with other systems of units, the units of a set of natural units will include definitions and values for length, mass, time, temperature. It is possible to disregard temperature as a physical quantity, since it states the energy per degree of freedom of a particle. Virtually every system of natural units normalizes Boltzmanns constant kB to 1, there are two common ways to relate charge to mass, length, and time, In Lorentz–Heaviside units, Coulombs law is F = q1q2/4πr2, and in Gaussian units, Coulombs law is F = q1q2/r2. Both possibilities are incorporated into different natural unit systems, where, α is the fine-structure constant,2 ≈0.007297, αG is the gravitational coupling constant,2 ≈ 6955175200000000000♠1. 752×10−45. Natural units are most commonly used by setting the units to one, for example, many natural unit systems include the equation c =1 in the unit-system definition, where c is the speed of light. If a velocity v is half the speed of light, then as v = c/2 and c =1, the equation v = 1/2 means the velocity v has the value one-half when measured in Planck units, or the velocity v is one-half the Planck unit of velocity. The equation c =1 can be plugged in anywhere else, for example, Einsteins equation E = mc2 can be rewritten in Planck units as E = m. This equation means The energy of a particle, measured in Planck units of energy, equals the mass of the particle, measured in Planck units of mass. For example, the special relativity equation E2 = p2c2 + m2c4 appears somewhat complicated, Physical interpretation, Natural unit systems automatically subsume dimensional analysis. For example, in Planck units, the units are defined by properties of quantum mechanics, not coincidentally, the Planck unit of length is approximately the distance at which quantum gravity effects become important. Likewise, atomic units are based on the mass and charge of an electron, no prototypes, A prototype is a physical object that defines a unit, such as the International Prototype Kilogram, a physical cylinder of metal whose mass is by definition exactly one kilogram. A prototype definition always has imperfect reproducibility between different places and between different times, and it is an advantage of natural systems that they use no prototypes. Less precise measurements, SI units are designed to be used in precision measurements, for example, the second is defined by an atomic transition frequency in cesium atoms, because this transition frequency can be precisely reproduced with atomic clock technology

Natural units
–

Base units
47.
Conversion of units
–
Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors. The process of conversion depends on the situation and the intended purpose. This may be governed by regulation, contract, technical specifications or other published standards, engineering judgment may include such factors as, The precision and accuracy of measurement and the associated uncertainty of measurement. The statistical confidence interval or tolerance interval of the initial measurement, the number of significant figures of the measurement. The intended use of the measurement including the engineering tolerances, historical definitions of the units and their derivatives used in old measurements, e. g. international foot vs. Some conversions from one system of units to another need to be exact and this is sometimes called soft conversion. It does not involve changing the configuration of the item being measured. By contrast, a conversion or an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable numbers and units in the new system and it sometimes involves a slightly different configuration, or size substitution, of the item. Nominal values are allowed and used. A conversion factor is used to change the units of a quantity without changing its value. The unity bracket method of unit conversion consists of a fraction in which the denominator is equal to the numerator, because of the identity property of multiplication, the value of a number will not change as long as it is multiplied by one. Also, if the numerator and denominator of a fraction are equal to each other, so as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity. There are many applications that offer the thousands of the various units with conversions. For example, the free software movement offers a command line utility GNU units for Linux and this article gives lists of conversion factors for each of a number of physical quantities, which are listed in the index. For each physical quantity, a number of different units are shown, Conversion between units in the metric system can be discerned by their prefixes and are thus not listed in this article. Exceptions are made if the unit is known by another name. Within each table, the units are listed alphabetically, and the SI units are highlighted, notes, See Weight for detail of mass/weight distinction and conversion

Conversion of units
–

Base units