TNT equivalent

Diagram of explosive yield vs mushroom cloud height, illustrating the difference between 22 kiloton Fat Man and 15 megaton Castle Bravo explosions

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 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

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

A gram of TNT releases 2673–6702 J (joules) upon explosion.^[3] The energy liberated by one gram of TNT was arbitrarily defined as a matter of convention to be 4184 J,^[4] which is exactly one kilocalorie.

An explosive's energy is normally expressed as the thermodynamic work produced by its detonation, which for TNT has been accurately measured as 4686 J/g from a large sample of air blast experiments, and theoretically calculated to be 4853 J/g.^[5]

The measured, pure heat output of a gram of TNT is only 2724 J,^[6] but this is not the important value for explosive blast effect calculations.

Alternative TNT equivalency can be calculated as a function of when in the detonation the value is measured and which property is being compared.^{[7][8][9][10]}

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

Conversion to other units

1 ton TNT equivalent is approximately:

• 1.0×10⁹ calories
• 4.184×10⁹ joules
• 3.96831×10⁶ British thermal units
• 3.08802×10⁹ foot pounds
• 1.162×10³ kilowatt hours

Examples

Megatons of TNT	Energy [Wh]	Description
6988100000000000000♠1×10−12 (i.e. 1 gram of TNT)	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.
6991100000000000000♠1×10−9 (i.e. 1 kilogram of TNT)	1.162 kWh	Under controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle.
6992100000000000000♠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]
6992120000000000000♠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]
6994100000000000000♠1×10−6 (i.e. 1 ton of TNT) – 6995440000000000000♠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]
6994189999999999999♠1.9×10−6	2.90 MWh	The television show MythBusters used 2.5 tons of ANFO to make "homemade" diamonds.
6996500000000000000♠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.
6997100000000000000♠1×10−3 (1 kiloton of TNT) – 6997200000000000000♠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.
6997230000000000000♠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).
6997300000000000000♠3×10−3	3.49 GWh	The Halifax Explosion in 1917 was the accidental detonation of 3,000 tons of TNT.
6997400000000000000♠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.
6998150000000000000♠1.5×10−2 – 6998200000000000000♠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, 50, 100	29 TWh, 58 TWh, 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 till now is about 540 megatons.
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.
6,000,000 = 7006600000000000000♠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.
7006932000000000000♠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 7022390000000000000♠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.
7006956000000000000♠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.
7008100000000000000♠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.
7015597200000000000♠5.972×1015	6.94 × 1027 Wh	The explosive energy of a quantity of TNT the mass of Earth.
7015789000000000000♠7.89×1015	9.17 × 1027 Wh	Total solar output in all directions per day.
7021198000000000000♠1.98×1021	2.3 × 1033 Wh	The explosive energy of a quantity of TNT the mass of the Sun.
7028239999999999999♠2.4×1028 – 7028479999999999999♠4.8×1028	2.8–5.6 × 1040 Wh	A type 1a supernova explosion gives off 1–7044200000000000000♠2×1044 joules of energy, which is about 2.4 to 4.8 hundred billion yottatons (24 to 48 octillion (2.4–7028479999999999999♠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.
7030240000000000000♠2.4×1030 – 7030480000000000000♠4.8×1030	2.8–7042560000000000000♠5.6×1042 Wh	The largest type of supernova observed, gamma-ray bursts (GRBs) release more than 1046 joules of energy.[28]
7032130000000000000♠1.3×1032	7044150000000000000♠1.5×1044 Wh	A merger of two black holes, first observation of gravitational waves, released 7047530000000000000♠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 1.0/0.42 (or 2.38) kg, respectively.

See also

• Brisance
• Net explosive quantity
• Nuclear weapon yield
• Orders of magnitude (energy)
• Relative effectiveness factor
• Table of explosive detonation velocities
• Ton
• Tonne
• Tonne of oil equivalent, a unit of energy almost exactly 10 tonnes of TNT

References

• Thompson, A.; Taylor, B.N. (July 2008). Guide for the Use of the International System of Units (SI). NIST Special Publication. 811. National Institute of Standards and Technology. Version 3.2.
• Nuclear Weapons FAQ Part 1.3
• Rhodes, Richard (2012). The Making of the Atomic Bomb (25th Anniversary ed.). Simon & Schuster. ISBN 978-1-4516-7761-4.
• Cooper, Paul W. (1996), Explosives Engineering, New York: Wiley-VCH, ISBN 0-471-18636-8
• HQ Department of the Army (2004) [1967], Field Manual 5-25: Explosives and Demolitions, Washington, D.C.: Pentagon Publishing, pp. 83–84, ISBN 0-9759009-5-1
• Explosives - Compositions, Alexandria, VA: GlobalSecurity.org, retrieved September 1, 2010
• Urbański, Tadeusz (1985) [1984], Chemistry and Technology of Explosives, Volumes I–IV (second ed.), Oxford: Pergamon
• Mathieu, Jörg; Stucki, Hans (2004), "Military High Explosives", CHIMIA International Journal for Chemistry, Schweizerische Chemische Gesellschaft, 58 (6): 383–389, doi:10.2533/000942904777677669, ISSN 0009-4293
• 3. Thermobaric Explosives, Advanced Energetic Materials, 2004., The National Academies Press, nap.edu, 2004