TNT equivalent

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) of TNT. In other words, for each gram of TNT exploded, 4184 joules (or one large Calorie = 1,000 calories) of energy is released.

"Kiloton" redirects here. For the similarly named weight measurements, see Tonne.
Ton of TNT
The explosion from a 14 kiloton nuclear test at the Nevada Test Site, in 1951.
General information
Unit systemNon-standard
Unit ofenergy
Symbolt or ton of TNT
Conversions
1 t in ...... is equal to ...
   SI base units   ≈ 4.184 gigajoules
   CGS   109 calories

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

The "kiloton (of TNT)" is a unit of energy equal to 4.184 terajoules (4.184×1012 J).

The "megaton (of TNT)" is a unit of energy equal to 4.184 petajoules (4.184×1015 J).

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

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 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 (6.3×1013 J); but an actual explosion of a 15000 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
milligram of TNT mg nanoton of TNT nt 4.184 J or 4.184 joules 1.162 mWh 46.55 fg
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

1 ton TNT equivalent is approximately:

Examples
Further information: Orders of magnitude (energy)
Megatons of TNT Energy [Wh] Description
1×10−12 1.162 Wh ≈ 1 food Calorie (large Calorie, kcal), 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]
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 2.088 GWh Estimated yield of the Beirut explosion of 2,750 tons of ammonium nitrate[14] that killed initially 137 at and near a Lebanese port at 6 p.m. local time Tuesday August 4, 2020.[15] An independent study by experts from the Blast and Impact Research Group at the University of Sheffield predicts the best estimate of the yield of Beirut explosion to be 0.5 kilotons of TNT and the reasonable bound estimate as 1.12 kilotons of TNT.[16]
(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).
2.9×10−3 3.49 GWh The Halifax Explosion in 1917 was the accidental detonation of 200 tons of TNT and 2,300 tons of Picric acid
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,[17] 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) killing between 90,000 and 166,000 people,[18] 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) killing over 60,000.[18] 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.[19] 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.[20]
4 4.6 TWh The biggest H-bomb that China has detonated is 4 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.[21]
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.[22] 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.
100 29–116 TWh 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).[23] 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 1883 eruption of Krakatoa in the Dutch East Indies (present-day Indonesia).
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.
1,460 1.69 PWh The total global nuclear arsenal is about 15,000 nuclear warheads[24][25][26] with a destructive capacity of around 1460 megatons[27][28][29][30] or 1.460 gigatons (1,460 million tons) of TNT. This is the equivalent of 6.11x1021 joules of energy
33,000 38 PWh The total energy released by the 1815 eruption of Mount Tambora in the island of Sumbawa in Indonesia.
104,400 121 PWh The total solar irradience energy received by Earth in the upper atmosphere per hour.
875,000 1,000 PWh Approximate yield of the last eruption of the Yellowstone supervolcano.
2.39×106 2,673 PWh Approximate total yield of the super eruption of the La Garita Caldera was the second most energetic event to have occurred on Earth since the Cretaceous–Paleogene extinction event 65–66 million years ago. The asteroid impact responsible for that mass-extinction, equivalent to 100 teratons of TNT.
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,[31] slightly less than the 2004 Indian Ocean quake. This is equivalent to 9.32 teratons of TNT.
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). 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 kilometres of the impact in a split second. Such energy is equivalent to that needed to power the whole Earth for several centuries.
3×108 - 119×108 349 EWh to 14 ZWh Later estimates for the Chicxulub impactor energy have climbed to between 300 million megatons and 11,900 million megatons.[32]
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. This is the astrophysical standard candle used to determine galactic distances.
(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.[33]
1.3×1032 1.5×1044 Wh A merger of two black holes, resulting in the first observation of gravitational waves, released 5.3×1047 joules

Relative effectiveness factor

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 1.0/0.32 (or 3.125) kg, respectively.

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

Some relative effectiveness factor examples
Explosive, grade Density
(g/ml)		 Detonation
vel. (m/s)		 Relative
effectiveness
Ammonium nitrate (AN + <0.5% H2O) 0.88 2700[34] 0.32[35][36]
Mercury(II) fulminate 4.42 4250 0.51[37]
Black powder (75% KNO3 + 19% C + 6% S, ancient explosives) 1.65 600 0.55[38]
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) 1.70 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 1.37
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 7700 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) 1.77 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
Hexanitrohexaazaisowurtzitane (HNIW; AKA 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
Nuclear weapons and the most powerful non-nuclear weapon examples
Weapon Total yield
(kilotons of TNT)		 Weight
(kg)		 Relative
effectiveness
Bomb used in Oklahoma City (ANFO based on racing fuel) 0.0018 2,300 0.78
GBU-57 bomb (Massive Ordnance Penetrator, MOP) 0.0035 13,600 0.26
Grand Slam (Earthquake bomb, M110) 0.0065 9,900 0.66
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
W54, Mk-54 (Davy Crockett) 0.022 23 1,000
W54, B54 (SADM) 1.0 23 43,500
Hypothetical suitcase nuke 2.5 31 80,000
Fat Man (dropped on Nagasaki) A-bomb 20 4600 4,500
Classic (one-stage) fission A-bomb 22 420 50,000
W88 modern thermonuclear warhead (MIRV) 470 355 1,300,000
Typical (two-stage) nuclear bomb 500–1000 650–1120 900,000
W56 thermonuclear warhead 1,200 272–308 4,960,000
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

See also

References
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