# SI derived unit

**SI derived units** are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless, or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m^{2}), the SI derived unit of area; and the kilogram per cubic metre (kg/m^{3} or kg m^{−3}), the SI derived unit of density.

The names of SI derived units, when written in full, are in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter, for example, the symbol for hertz is "Hz"; but the symbol for metre is "m".^{[1]}

## Contents

## Derived units with special names[edit]

The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).

Name | Symbol | Quantity | Equivalents | SI base unit Equivalents |
---|---|---|---|---|

hertz | Hz | frequency | 1/s | s^{−1} |

radian | rad | angle | m/m | 1 |

steradian | sr | solid angle | m^{2}/m^{2} |
1 |

newton | N | force, weight | kg⋅m/s^{2} |
kg⋅m⋅s^{−2} |

pascal | Pa | pressure, stress | N/m^{2} |
kg⋅m^{−1}⋅s^{−2} |

joule | J | energy, work, heat | N⋅m C⋅V W⋅s |
kg⋅m^{2}⋅s^{−2} |

watt | W | power, radiant flux | J/s V⋅A |
kg⋅m^{2}⋅s^{−3} |

coulomb | C | electric charge or quantity of electricity | s⋅A F⋅V |
s⋅A |

volt | V | voltage, electrical potential difference, electromotive force | W/A J/C |
kg⋅m^{2}⋅s^{−3}⋅A^{−1} |

farad | F | electrical capacitance | C/V s/Ω |
kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} |

ohm | Ω | electrical resistance, impedance, reactance | 1/S V/A |
kg⋅m^{2}⋅s^{−3}⋅A^{−2} |

siemens | S | electrical conductance | 1/Ω A/V |
kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |

weber | Wb | magnetic flux | J/A T⋅m ^{2} |
kg⋅m^{2}⋅s^{−2}⋅A^{−1} |

tesla | T | magnetic field strength, magnetic flux density | V⋅s/m^{2}Wb/m ^{2}N/(A⋅m) |
kg⋅s^{−2}⋅A^{−1} |

henry | H | electrical inductance | V⋅s/A Ω⋅s Wb/A |
kg⋅m^{2}⋅s^{−2}⋅A^{−2} |

degree Celsius | °C | temperature relative to 273.15 K | K | K |

lumen | lm | luminous flux | cd⋅sr | cd |

lux | lx | illuminance | lm/m^{2} |
m^{−2}⋅cd |

becquerel | Bq | radioactivity (decays per unit time) | 1/s | s^{−1} |

gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |

sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |

katal | kat | catalytic activity | mol/s | s^{−1}⋅mol |

## Examples of derived quantities and units[edit]

Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|

square metre | m^{2} |
area | m^{2} |

cubic metre | m^{3} |
volume | m^{3} |

metre per second | m/s | speed, velocity | m⋅s^{−1} |

cubic metre per second | m^{3}/s |
volumetric flow | m^{3}⋅s^{−1} |

metre per second squared | m/s^{2} |
acceleration | m⋅s^{−2} |

metre per second cubed | m/s^{3} |
jerk, jolt | m⋅s^{−3} |

metre per second to the fourth | m/s^{4} |
snap, jounce | m⋅s^{−4} |

radian per second | rad/s | angular velocity | s^{−1} |

radian per second squared | rad/s^{2} |
angular acceleration | s^{−2} |

newton second | N⋅s | momentum, impulse | m⋅kg⋅s^{−1} |

newton metre second | N⋅m⋅s | angular momentum | m^{2}⋅kg⋅s^{−1} |

newton metre | N⋅m = J/rad | torque, moment of force | m^{2}⋅kg⋅s^{−2} |

newton per second | N/s | yank | m⋅kg⋅s^{−3} |

reciprocal metre | m^{−1} |
wavenumber, optical power, curvature, spatial frequency | m^{−1} |

kilogram per square metre | kg/m^{2} |
area density | m^{−2}⋅kg |

kilogram per cubic metre | kg/m^{3} |
density, mass density | m^{−3}⋅kg |

cubic metre per kilogram | m^{3}/kg |
specific volume | m^{3}⋅kg^{−1} |

mole per cubic metre | mol/m^{3} |
molarity, amount of substance concentration | m^{−3}⋅mol |

cubic metre per mole | m^{3}/mol |
molar volume | m^{3}⋅mol^{−1} |

joule second | J⋅s | action | m^{2}⋅kg⋅s^{−1} |

joule per kelvin | J/K | heat capacity, entropy | m^{2}⋅kg⋅s^{−2}⋅K^{−1} |

joule per kelvin mole | J/(K⋅mol) | molar heat capacity, molar entropy | m^{2}⋅kg⋅s^{−2}⋅K^{−1}⋅mol^{−1} |

joule per kilogram kelvin | J/(K⋅kg) | specific heat capacity, specific entropy | m^{2}⋅s^{−2}⋅K^{−1} |

joule per mole | J/mol | molar energy | m^{2}⋅kg⋅s^{−2}⋅mol^{−1} |

joule per kilogram | J/kg | specific energy | m^{2}⋅s^{−2} |

joule per cubic metre | J/m^{3} |
energy density | m^{−1}⋅kg⋅s^{−2} |

newton per metre | N/m = J/m^{2} |
surface tension, stiffness | kg⋅s^{−2} |

watt per square metre | W/m^{2} |
heat flux density, irradiance | kg⋅s^{−3} |

watt per metre kelvin | W/(m⋅K) | thermal conductivity | m⋅kg⋅s^{−3}⋅K^{−1} |

square metre per second | m^{2}/s |
kinematic viscosity, thermal diffusivity, diffusion coefficient | m^{2}⋅s^{−1} |

pascal second | Pa⋅s = N⋅s/m^{2} |
dynamic viscosity | m^{−1}⋅kg⋅s^{−1} |

coulomb per square metre | C/m^{2} |
electric displacement field, polarization density | m^{−2}⋅s⋅A |

coulomb per cubic metre | C/m^{3} |
electric charge density | m^{−3}⋅s⋅A |

ampere per square metre | A/m^{2} |
electric current density | m^{−2}⋅A |

siemens per metre | S/m | electrical conductivity | m^{−3}⋅kg^{−1}⋅s^{3}⋅A^{2} |

siemens square metre per mole | S⋅m^{2}/mol |
molar conductivity | kg^{−1}⋅s^{3}⋅A^{2}⋅mol^{−1} |

farad per metre | F/m | permittivity | m^{−3}⋅kg^{−1}⋅s^{4}⋅A^{2} |

henry per metre | H/m | magnetic permeability | m⋅kg⋅s^{−2}⋅A^{−2} |

volt per metre | V/m | electric field strength | m⋅kg⋅s^{−3}⋅A^{−1} |

ampere per metre | A/m | magnetization, magnetic field strength | m^{−1}⋅A |

candela per square metre | cd/m^{2} |
luminance | m^{−2}⋅cd |

lumen second | lm⋅s | luminous energy | s⋅cd⋅sr |

lux second | lx⋅s | luminous exposure | m^{−2}⋅s⋅cd⋅sr |

coulomb per kilogram | C/kg | exposure (X and gamma rays) | kg^{−1}⋅s⋅A |

gray per second | Gy/s | absorbed dose rate | m^{2}⋅s^{−3} |

ohm metre | Ω⋅m | resistivity | m^{3}⋅kg⋅s^{−3}⋅A^{−2} |

kilogram per metre | kg/m | linear mass density | m^{−1}⋅kg |

coulomb per metre | C/m | linear charge density | m^{−1}⋅s⋅A |

mole per kilogram | mol/kg | molality | kg^{−1}⋅mol |

kilogram per mole | kg/mol | molar mass | kg⋅mol^{−1} |

metre per cubic metre | m/m^{3} |
fuel efficiency | m^{−2} |

kilogram per second | kg/s | mass flow rate | kg⋅s^{−1} |

joule per tesla | J/T | magnetic dipole moment | m^{2}⋅A |

watt per cubic metre | W/m^{3} |
spectral irradiance, power density | m^{−1}⋅kg⋅s^{−3} |

kelvin per watt | K/W | thermal resistance | m^{−2}⋅kg^{−1}⋅s^{3}⋅K |

reciprocal kelvin | K^{−1} |
thermal expansion coefficient | K^{−1} |

kelvin per metre | K/m | temperature gradient | m^{−1}⋅K |

square metre per volt second | m^{2}/(V⋅s) |
electron mobility | kg^{−1}⋅s^{2}⋅A |

joule per square metre second | J/(m^{2}⋅s) |
energy flux density | kg⋅s^{−3} |

reciprocal pascal | Pa^{−1} |
compressibility | m⋅kg^{−1}⋅s^{2} |

reciprocal henry | H^{−1} |
magnetic reluctance | m^{−2}⋅kg^{−1}⋅s^{2}⋅A^{2} |

weber per metre | Wb/m | magnetic vector potential | m⋅kg⋅s^{−2}⋅A^{−1} |

weber metre | Wb⋅m | magnetic moment | m^{3}⋅kg⋅s^{−2}⋅A^{−1} |

tesla metre | T⋅m | magnetic rigidity | m⋅kg⋅s^{−2}⋅A^{−1} |

joule per square metre | J/m^{2} |
radiant exposure | kg⋅s^{−2} |

cubic metre per mole second | m^{3}/(mol⋅s) |
catalytic efficiency | m^{3}⋅s^{−1}⋅mol^{−1} |

kilogram square metre | kg⋅m^{2} |
moment of inertia | m^{2}⋅kg |

newton metre second per kilogram | N⋅m⋅s/kg | specific angular momentum | m^{2}⋅s^{−1} |

hertz per second | Hz/s | frequency drift | s^{−2} |

lumen per watt | lm/W | luminous efficacy | m^{−2}⋅kg^{−1}⋅s^{3}⋅cd⋅sr |

ampere radian | A⋅rad | magnetomotive force | A |

metre per henry | m/H | magnetic susceptibility | m^{−1}⋅kg^{−1}⋅s^{2}⋅A^{2} |

watt per steradian | W/sr | radiant intensity | m^{2}⋅kg⋅s^{−3} |

watt per steradian metre | W/(sr⋅m) | spectral intensity | m⋅kg⋅s^{−3} |

watt per steradian square metre | W/(sr⋅m^{2}) |
radiance | kg⋅s^{−3} |

watt per steradian cubic metre | W/(sr⋅m^{3}) |
spectral radiance | m^{−1}⋅kg⋅s^{−3} |

watt per metre | W/m | spectral power | m⋅kg⋅s^{−3} |

## Other units used with SI[edit]

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.

## Supplementary units[edit]

Until 1995, the SI classified the radian and the steradian as *supplementary units*, but this designation was abandoned and the units were grouped as derived units.^{[3]}

## See also[edit]

- International System of Quantities (ISQ)
- International Vocabulary of Metrology
- Metric prefix
- Metric system
- Planck units

## References[edit]

**^**Suplee, Curt (2 July 2009). "Special Publication 811".**^**International Bureau of Weights and Measures (2006),*The International System of Units (SI)*(PDF) (8th ed.), ISBN 92-822-2213-6, archived (PDF) from the original on 2017-08-14**^**"Resolution 8 of the CGPM at its 20th Meeting (1995)". Bureau International des Poids et Mesures. Retrieved 2014-09-23.

## Bibliography[edit]

- I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June 1993).
*Quantities, Units and Symbols in Physical Chemistry*(2nd ed.). Blackwell Science Inc. p. 72.