TNT equivalent

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"Kiloton" redirects here. For the similarly named weight measurements, see Tonne.
Diagram of explosive yield vs mushroom cloud height, illustrating the difference between 22 kiloton Fat Man and 15 megaton Castle Bravo explosions[citation needed]

TNT equivalent is a convention for expressing energy, typically used to describe the energy released in an explosion. The "ton of TNT" is a unit of energy defined by that convention to be 4.184 gigajoules,[1] which is the approximate energy released in the detonation of a metric ton (1,000 kilograms or one megagram) of TNT. In other words, for each gram of TNT exploded, 4,184 joules (or one large calorie = 1,000 calories) of energy are released.

This convention intends to compare the destructiveness of an event with that of traditional explosive materials, of which TNT is a typical example, although other conventional explosives such as dynamite contain more energy.

Kiloton and megaton[edit]

The "kiloton (of TNT)" is a unit of energy equal to 4.184 terajoules.

The "megaton (of TNT)" is a unit of energy equal to 4.184 petajoules.

The kiloton and megaton of TNT have traditionally been used to describe the energy output, and hence the destructive power, of a nuclear weapon. The TNT equivalent appears in various nuclear weapon control treaties, and has been used to characterize the energy released in such other highly destructive events as an asteroid impact.[2]

Historical derivation of the value[edit]

Alternative values for TNT equivalency can be calculated according to which property is being compared and when in the two detonation processes the values are measured.[3][4][5][6]

Where for example the comparison is by energy yield, an explosive's energy is normally expressed for chemical purposes as the thermodynamic work produced by its detonation. For TNT this has been accurately measured as 4686 J/g from a large sample of air blast experiments, and theoretically calculated to be 4853 J/g.[7]

But, even on this basis, comparing the actual energy yields of a large nuclear device and an explosion of TNT can be slightly inaccurate. Small TNT explosions, especially in the open, don't tend to burn the carbon-particle and hydrocarbon products of the explosion. Gas-expansion and pressure-change effects tend to "freeze" the burn rapidly. A large open explosion of TNT may maintain fireball temperatures high enough so that some of those products do burn up with atmospheric oxygen.[8]

Such differences can be substantial. For safety purposes a range as wide as 2673–6702 J (joules) has been stated for a gram of TNT upon explosion.[9]

So, one can state that a nuclear bomb has a yield of 15 kt (63×1012 or 6.3×1013 J); but an actual explosion of a 15 000 ton pile of TNT may yield (for example) 8×1013 J due to additional carbon/hydrocarbon oxidation not present with small open-air charges.[8]

These complications have been sidestepped by convention. The energy liberated by one gram of TNT was arbitrarily defined as a matter of convention to be 4184 J,[10] which is exactly one kilocalorie.

A kiloton of TNT can be visualized as a cube of TNT 8.46 metres (27.8 ft) on a side.

Grams TNT Symbol Tons TNT Symbol Energy [Joules] Energy [Wh] Corresponding mass loss
gram of TNT g microton of TNT μt 4.184×103 J or 4.184 kilojoules 1.162 Wh 46.55 pg
kilogram of TNT kg milliton of TNT mt 4.184×106 J or 4.184 megajoules 1.162 kWh 46.55 ng
megagram of TNT Mg ton of TNT t 4.184×109 J or 4.184 gigajoules 1.162 MWh 46.55 μg
gigagram of TNT Gg kiloton of TNT kt 4.184×1012 J or 4.184 terajoules 1.162 GWh 46.55 mg
teragram of TNT Tg megaton of TNT Mt 4.184×1015 J or 4.184 petajoules 1.162 TWh 46.55 g
petagram of TNT Pg gigaton of TNT Gt 4.184×1018 J or 4.184 exajoules 1.162 PWh 46.55 kg

Conversion to other units[edit]

1 ton TNT equivalent is approximately:

Examples[edit]

Further information: Orders of magnitude (energy)
Megatons of TNT Energy [Wh] Description
1×10−12 1.162 Wh ≈ 1 food Calorie (large calorie), which is the approximate amount of energy needed to raise the temperature of one kilogram of water by one degree Celsius at a pressure of one atmosphere.
1×10−9 1.162 kWh Under controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle.
1×10−8 11.62 kWh The approximate radiant heat energy released during 3-phase, 600 V, 100 kA arcing fault in a 0.5 m × 0.5 m × 0.5 m (20 in × 20 in × 20 in) compartment within a 1-second period.[11][further explanation needed]
1.2×10−8 13.94 kWh Amount of TNT used (12 kg) in Coptic church explosion in Cairo, Egypt on December 11, 2016 that left 25 dead[12]
(1–44)×10−6 1.16–51.14 MWh Conventional bombs yield from less than one ton to FOAB's 44 tons. The yield of a Tomahawk cruise missile is equivalent to 500 kg of TNT, or approximately 0.5 tons.[13]
1.9×10−6 2.90 MWh The television show MythBusters used 2.5 tons of ANFO to make "homemade" diamonds.
5×10−4 581 MWh A real 0.5-kilotonne-of-TNT (2.1 TJ) charge at Operation Sailor Hat. If the charge were a full sphere, it would be 1 kilotonne of TNT (4.2 TJ).
500 tons of TNT (5 by 10 m (17 by 34 ft)) awaiting detonation at Operation Sailor Hat.
(1–2)×10−3 1.16–2.32 GWh Estimated yield of the Oppau explosion that killed more than 500 at a German fertilizer factory in 1921.
2.3×10−3 2.67 GWh Amount of solar energy falling on 4,000 m2 (1 acre) of land in a year is 9.5 TJ (2,650 MWh) (an average over the Earth's surface).
3×10−3 3.49 GWh The Halifax Explosion in 1917 was the accidental detonation of 3,000 tons of TNT.
4×10−3 9.3 GWh Minor Scale, a 1985 United States conventional explosion, using 4,744 tons of ANFO explosive to provide a scaled equivalent airblast of an eight kiloton (33.44 TJ) nuclear device,[14] is believed to be the largest planned detonation of conventional explosives in history.
(1.5–2)×10−2 17.4–23.2 GWh The Little Boy atomic bomb dropped on Hiroshima on August 6, 1945, exploded with an energy of about 15 kilotons of TNT (63 TJ), and the Fat Man atomic bomb dropped on Nagasaki on August 9, 1945, exploded with an energy of about 20 kilotons of TNT (84 TJ). The modern nuclear weapons in the United States arsenal range in yield from 0.3 kt (1.3 TJ) to 1.2 Mt (5.0 PJ) equivalent, for the B83 strategic bomb.
1 1.16 TWh The energy contained in one megaton of TNT (4.2 PJ) is enough to power the average American household for 103,000 years.[15] The 30 Mt (130 PJ) estimated upper limit blast power of the Tunguska event could power the same average home for more than 3,100,000 years. The energy of that blast could power the entire United States for 3.27 days.[16]
3 3.5 TWh The total energy of all explosives used in World War II, including the Hiroshima and Nagasaki atom bombs, is estimated to have been three megatons of TNT.
8.6 10 TWh The energy released by a typical tropical cyclone in one minute, primarily from water condensation. Winds constitute 0.25% of that energy.[17]
21.5 25 TWh The complete conversion of 1 kg of matter into pure energy would yield the theoretical maximum (E = mc2) of 89.8 petajoules, which is equivalent to 21.5 megatons of TNT. No such method of total conversion as combining 500 grams of matter with 500 grams of antimatter has yet been achieved. In the event of proton–antiproton annihilation, approximately 50% of the released energy will escape in the form of neutrinos, which are almost undetectable.[18] Electron–positron annihilation events emit their energy entirely as gamma rays.
24 28 TWh Approximate total yield of the 1980 eruption of Mount St. Helens.
25–100 29–116 TWh During the Cold War, the United States developed hydrogen bombs with maximum theoretical yields of 25 megatons of TNT (100 PJ). The Soviet Union developed a prototype weapon, nicknamed the Tsar Bomba, which was tested at 50 Mt (210 PJ), but had a maximum theoretical yield of 100 Mt (420 PJ).[19] The effective destructive potential of such a weapon varies greatly, depending on such conditions as the altitude at which it is detonated, the characteristics of the target, the terrain, and the physical landscape upon which it is detonated.
26.3 30.6 TWh Megathrust earthquakes 2004 Indian Ocean earthquake released record ME surface rupture energy, or potential for damage at 26.3 megatons of TNT (110 PJ).
200 232 TWh The total energy released by the eruption of Mt. Krakatoa in Indonesia in 1883.
540 628 TWh The total energy produced worldwide by all nuclear testing and combat combined, from the 1940s until the present is about 540 megatons.[citation needed]
1,460 1.69 PWh The total global nuclear arsenal is about 15,000 nuclear warheads[20][21][22] with a destructive capacity of around 1460 megatons[23][24][25][26] or 1.460 gigatons (1,460 million tons) of TNT.
62,500 73 PWh The total solar energy received by Earth per minute is 440 exajoules.
875,000 1,000 PWh Approximate yield of the last eruption of the Yellowstone supervolcano.
6×106 6,973 PWh The estimated energy at impact when the largest fragment of Comet Shoemaker–Levy 9 struck Jupiter is equivalent to 6 million megatons (6 trillion tons) of TNT.
9.32×106 10,831 PWh The energy released in the 2011 Tōhoku earthquake and tsunami was over 200,000 times the surface energy and was calculated by the USGS at 3.9×1022 joules,[27] slightly less than the 2004 Indian Ocean quake. This is equivalent to 9,320 gigatons of TNT, or approximately 600 million times the energy of the Hiroshima bomb.
9.56×106 11,110 PWh Megathrust earthquakes record huge MW values, or total energy released. The 2004 Indian Ocean earthquake released 9,560 gigatons TNT equivalent.
1×108 116,222 PWh The approximate energy released when the Chicxulub impact caused the mass extinction 65-66 million years ago was estimated to be equal to 100 teratons (i.e. 100 exagrams or approximately 220.462 quadrillion pounds) of TNT (a teraton equals 1 million megatons). That is roughly 8 billion times stronger than each of the bombs that hit Hiroshima and Nagasaki and the most energetic event on the history of Earth for hundreds of millions of years, far more powerful than any volcanic eruption, earthquake or firestorm. Such an explosion annihilated everything within a thousand miles of the impact in a split second. Such energy is equivalent to that needed to power the whole Earth for several centuries.
5.972×1015 6.94×1027 Wh The explosive energy of a quantity of TNT the mass of Earth.
7.89×1015 9.17×1027 Wh Total solar output in all directions per day.
1.98×1021 2.3×1033 Wh The explosive energy of a quantity of TNT the mass of the Sun.
(2.4–4.8)×1028 (2.8–5.6)×1040 Wh A type 1a supernova explosion gives off 1–2×1044 joules of energy, which is about 2.4–4.8 hundred billion yottatons (24–48 octillion (2.4–4.8×1028) megatons) of TNT, equivalent to the explosive force of a quantity of TNT over a trillion (1012) times the mass of the planet Earth.
(2.4–4.8)×1030 (2.8–5.6)×1042 Wh The largest type of supernova observed, gamma-ray bursts (GRBs) release more than 1046 joules of energy.[28]
1.3×1032 1.5×1044 Wh A merger of two black holes, first observation of gravitational waves, released 5.3×1047 joules

Relative effectiveness factor[edit]

The relative effectiveness factor (RE factor) relates an explosive's demolition power to that of TNT, in units of the TNT equivalent/kg (TNTe/kg). The RE factor is the relative mass of TNT to which an explosive is equivalent: The greater the RE, the more powerful the explosive.

This enables engineers to determine the proper masses of different explosives when applying blasting formulas developed specifically for TNT. For example, if a timber-cutting formula calls for a charge of 1 kg of TNT, then based on octanitrocubane's RE factor of 2.38, it would take only 1.0/2.38 (or 0.42) kg of it to do the same job. Using PETN, engineers would need 1.0/1.66 (or 0.60) kg to obtain the same effects as 1 kg of TNT. With ANFO or ammonium nitrate, they would require 1.0/0.74 (or 1.35) kg or 1.0/0.42 (or 2.38) kg, respectively.

Calculating a single RE factor for a explosive is, however, impossible. It depends on the specific case of use. Given a pair of explosives, one can produce 2× the shockwave output (this itself extremely depends on the distance of measuring instruments) but the difference in direct metal cutting ability maybe 4× higher for one type of metal and 7× higher for another type of metal. The relative differences between two explosives in shaped charges will be even greater. The table below should be taken as an example and not as a precise source of data.

RE factor examples[edit]

Some RE factor examples
Explosive, grade Density
(g/ml) 		Detonation
vel. (m/s) 		R.E.
Ammonium nitrate (AN + <0.5% H2O) 0.88 2700[29] 0.42
Black powder (75% KNO3 + 19% C + 6% S, ancient explosives) 1.65 600 0.50
Mercury(II) fulminate 4.42 4250 0.51[30]
Tanerit Simply (93% granulated AN + 6% red P + 1% C) 0.90 2750 0.55
Hexamine dinitrate (HDN) 1.30 5070 0.60
Dinitrobenzene (DNB) 1.50 6025 0.60
HMTD (hexamine peroxide) 0.88 4520 0.74
ANFO (94% AN + 6% fuel oil) 0.92 5270 0.74
TATP (acetone peroxide) 1.18 5300 0.80
Tovex Extra (AN water gel) commercial product 1.33 5690 0.80
Hydromite 600 (AN water emulsion) commercial product 1.24 5550 0.80
ANNMAL (66% AN + 25% NM + 5% Al + 3% C + 1% TETA) 1.16 5360 0.87
Amatol (50% TNT + 50% AN) 1.50 6290 0.91
Nitroguanidine 1.32 6750 0.95
Trinitrotoluene (TNT) 1.60 6900 1.00
Hexanitrostilbene (HNS) 1.70 7080 1.05
Nitrourea 1.45 6860 1.05
Tritonal (80% TNT + 20% aluminium)* 1.70 6650 1.05
Nickel hydrazine nitrate (NHN) 2.12 7000 1.05
Amatol (80% TNT + 20% AN) 1.55 6570 1.10
Nitrocellulose (13.5% N, NC; AKA guncotton) 1.40 6400 1.10
Nitromethane (NM) 1.13 6360 1.10
PBXW-126 (22% NTO, 20% RDX, 20% AP, 26% Al, 12% PU's system)* 1.80 6450 1.10
Diethylene glycol dinitrate (DEGDN) 1.38 6610 1.17
PBXIH-135 EB (42% HMX, 33% Al, 25% PCP-TMETN's system)* 1.81 7060 1.17
PBXN-109 (64% RDX, 20% Al, 16% HTPB's system)* 1.68 7450 1.17
Triaminotrinitrobenzene (TATB) 1.80 7550 1.17
Picric acid (TNP) 1.71 7350 1.17
Trinitrobenzene (TNB) 1.60 7300 1.20
Tetrytol (70% tetryl + 30% TNT) 1.60 7370 1.20
Dynamite, Nobel's (75% NG + 23% diatomite) 1.48 7200 1.25
Tetryl 1.71 7770 1.25
Torpex (aka HBX, 41% RDX + 40% TNT + 18% Al + 1% wax)* 1.80 7440 1.30
Composition B (63% RDX + 36% TNT + 1% wax) 1.72 7840 1.33
Composition C-3 (78% RDX) 1.60 7630 1.33
Composition C-4 (91% RDX) 1.59 8040 1.34
Pentolite (56% PETN + 44% TNT) 1.66 7520 1.33
Semtex 1A (76% PETN + 6% RDX) 1.55 7670 1.35
Hexal (76% RDX + 20% Al + 4% wax)* 1.79 7640 1.35
RISAL P (50% IPN + 28% RDX + 15% Al + 4% Mg + 1% Zr + 2% NC)* 1.39 5980 1.40
Hydrazine mononitrate 1.59 8500 1.42
Mixture: 24% nitrobenzene + 76% TNM 1.48 8060 1.50
Mixture: 30% nitrobenzene + 70% nitrogen tetroxide 1.39 8290 1.50
Nitroglycerin (NG) 1.59 8100 1.54
Methyl nitrate (MN) 1.21 7900 1.54
Octol (80% HMX + 19% TNT + 1% DNT) 1.83 8690 1.54
Nitrotriazolon (NTO) 1.87 8120 1.60
DADNE (1,1-diamino-2,2-dinitroethene, FOX-7) 1.77 8330 1.60
Gelignite (92% NG + 7% nitrocellulose) 1.60 7970 1.60
Plastics Gel® (in toothpaste tube: 45% PETN + 45% NG + 5% DEGDN + 4% NC) 1.51 7940 1.60
Composition A-5 (98% RDX + 2% stearic acid) 1.65 8470 1.60
Erythritol tetranitrate (ETN) 1.72 8206 1.60
Hexogen (RDX) 1.78 8700 1.60
PBXW-11 (96% HMX, 1% HyTemp, 3% DOA) 1.81 8720 1.60
Penthrite (PETN) 1.71 8400 1.66
Ethylene glycol dinitrate (EGDN) 1.49 8300 1.66
Trinitroazetidine (TNAZ) 1.85 8640 1.70
Octogen (HMX grade B) 1.86 9100 1.70
HNIW (CL-20) 1.97 9380 1.80
Hexanitrobenzene (HNB) 1.97 9400 1.85
MEDINA (Methylene dinitroamine) 1.65 8700 1.93
DDF (4,4’-Dinitro-3,3’-diazenofuroxan) 1.98 10000 1.95
Heptanitrocubane (HNC) 1.92 9200 N/A
Octanitrocubane (ONC) 1.95 10600 2.38

*: TBX (thermobaric explosives) or EBX (enhanced blast explosives), in a small, confined space, may have over twice the power of destruction. The total power of aluminized mixtures strictly depends on the condition of explosions.

Nuclear examples[edit]

Nuclear weapons and the most powerful non-nuclear weapon examples
Weapon Total yield
(kilotons of TNT) 		Weight
(kg) 		R.E. ~
Davy Crockett (nuclear device) 0.022 23 1,000
Fat Man (dropped on Nagasaki) A-bomb 20 4600 4,500
Classic (one-stage) fission A-bomb 22 420 50,000
Hypothetical suitcase nuke 2.5 31 80,000
Typical (two-stage) nuclear bomb 500–1000 650–1120 900,000
W56 thermonuclear warhead 1,200 272–308 4,960,000
W88 modern thermonuclear warhead (MIRV) 470 355 1,300,000
B53 nuclear bomb (two-stage) 9,000 4050 2,200,000
B41 nuclear bomb (three-stage) 25,000 4850 5,100,000
Tsar nuclear bomb (three-stage) 50,000–56,000 26,500 2,100,000
GBU-57 bomb (Massive Ordnance Penetrator, MOP) 0.0035 13,600 0.26
Grand Slam (Earthquake bomb, M110) 0.0065 9,900 0.66
Bomb used in Oklahoma City (ANFO based on racing fuel) 0.0018 2,300 0.78
BLU-82 (Daisy Cutter) 0.0075 6,800 1.10
MOAB (non-nuclear bomb, GBU-43) 0.011 9,800 1.13
FOAB (advanced thermobaric bomb, ATBIP) 0.044 9,100 4.83

See also[edit]

References[edit]

  1. ^ "Tons (Explosives) to Gigajoules Conversion Calculator". unitconversion.org.
  2. ^ "Joules to Megatons Conversion Calculator". unitconversion.org.
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  5. ^ Maienschein, Jon L. (2002). Tnt equivalency of different explosives – estimation for calculating load limits in heaf firing tanks (Technical report). Lawrence Livermore National Laboratory. EMPE-02-22.
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  12. ^ Atassi, Basma; Sirgany, Sarah; Narayan, Chandrika (December 13, 2016). "Local media: Blast at Cairo cathedral kills at least 25". CNN. Retrieved 5 April 2017.
  13. ^ Homer-Dixon, Thomas F; Homer-Dixon, Thomas (2002). The Ingenuity Gap. p. 249. ISBN 978-0-375-71328-6.
  14. ^ TECH REPS INC ALBUQUERQUE NM (1986). "Minor Scale Event, Test Execution Report". hdl:100.2/ADA269600.
  15. ^ "Frequently Asked Questions – Electricity". United States Department of Energy. 2009-10-06. Retrieved 2009-10-21. (Calculated from 2007 value of 936 kWh monthly usage)
  16. ^ "Country Comparison :: Electricity – consumption". The World Factbook. CIA. Archived from the original on 2012-01-28. Retrieved 2009-10-22. (Calculated from 2007 value of 3,892,000,000,000 kWh annual usage)
  17. ^ "NOAA FAQ: How much energy does a hurricane release?". National Oceanic & Atmospheric Administration. August 2001. Retrieved 2009-06-30. cites 6E14 watts continuous.
  18. ^ Borowski, Stanley K. (March 1996). Comparison of Fusion/Antiproton Propulsion systems (PDF). 23rd Joint Propulsion Conference. NASA Glenn Research Center. doi:10.2514/6.1987-1814. hdl:2060/19960020441.[permanent dead link]
  19. ^ See Currently deployed U.S. nuclear weapon yields Archived September 7, 2016, at the Wayback Machine, Complete List of All U.S. Nuclear Weapons Archived December 16, 2008, at the Wayback Machine, Tsar Bomba Archived June 17, 2016, at the Wayback Machine, all from Carey Sublette's Nuclear Weapon Archive.
  20. ^ "Status of World Nuclear Forces". fas.org.
  21. ^ "Nuclear Weapons: Who Has What at a Glance". armscontrol.org.
  22. ^ "Global nuclear weapons: downsizing but modernizing". Stockholm International Peace Research Institute. 13 June 2016.
  23. ^ Kristensen, Hans M.; Norris, Robert S. (May 3, 2016). "Russian nuclear forces, 2016". Bulletin of the Atomic Scientists. 72 (3): 125–134. doi:10.1080/00963402.2016.1170359 – via Taylor and Francis+NEJM.
  24. ^ Kristensen, Hans M; Norris, Robert S (2015). "US nuclear forces, 2015". Bulletin of the Atomic Scientists. 71 (2): 107. doi:10.1177/0096340215571913.
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  27. ^ "USGS.gov: USGS WPhase Moment Solution". Earthquake.usgs.gov. Archived from the original on 13 March 2011. Retrieved 13 March 2011.
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  29. ^ US Army FM 3-34.214: Explosives and Demolition, 2007, page 1–2.
  30. ^ Whitehall Paraindistries
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