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 method of quantifying the energy released in explosions. The "ton of TNT" is a unit of energy equal to 4.184 gigajoules,^[1] which is approximately the amount of energy released in the detonation of a metric ton (1,000 kilograms or 1 megagram) of TNT. The "megaton of TNT" is a unit of energy equal to 4.184 petajoules.^[2]

The kiloton and megaton of TNT have traditionally been used to rate the energy output, and hence destructive power, of nuclear weapons (see nuclear weapon yield) and other high-energy events. This unit is written into various nuclear weapon control treaties, and gives a sense of destructiveness as compared with ordinary explosives, like TNT. More recently, it has been used to describe the energy released in other highly destructive events, such as asteroid impacts. However, TNT is not the most energetic of conventional explosives. Dynamite, for example, has about 60% more energy density (approximately 7.5 MJ/kg, compared to about 4.7 MJ/kg for TNT).

Historical derivation of the value

A gram of TNT releases 2673–6702 joules upon explosion.^[3] To define the ton of TNT, this was arbitrarily standardized by letting 1 gram TNT = 4184 J (exactly).^[4] This conveniently defined the energy liberated by one gram of TNT as exactly one kilocalorie.

This definition is a conventional one. The explosive's energy is normally calculated using the thermodynamic work energy of detonation, which for TNT has been accurately measured at 4686 J/g from large numbers 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 depending upon 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	Description
0.000000001	Under controlled conditions one kilogram of TNT can destroy (or even obliterate) a small vehicle.
0.00000001	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 time interval.[11]
0.000001–0.000044	Conventional bombs yield range from less than 1 ton to FOAB's 44 tonnes. The yield of a Tomahawk cruise missile is 500 kilograms of TNT equivalent, or approximately 0.55 tons.[12]
0.0000025	An American television show, MythBusters, used 2.5 tons of ANFO to make "homemade" diamonds.
0.0005	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 (6 by 12 m (20 by 40 ft)) awaiting detonation at Operation Sailor Hat.
0.001-0.002	Estimated yield of the Oppau explosion in 1921 at a German fertilizer factory, killing more than 500.
0.0023	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 disk).
0.003	The Halifax Explosion in 1917 involved the accidental detonation of 3,000 tons of TNT.
0.008	Minor Scale, a 1985 United States conventional explosion utilizing 4,744 tons of ANFO explosive to provide a scaled equivalent airblast of an 8 kiloton (33.44 TJ) nuclear device,[13] is believed to be the largest planned detonation of conventional explosives in history.
0.015–0.02	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 nuclear weapons currently in the arsenal of the United States range in yield from 0.3 kt (1.3 TJ) to 1.2 Mt (5.0 PJ) equivalent, for the B83 strategic bomb.
1	The energy contained in 1 megaton of TNT (4.2 PJ) is enough to power the average American household (in the year 2007) for 103,474 years.[14] For example, the 30 Mt (130 PJ) estimated upper limit blast power of the Tunguska event could power the aforementioned home for just over 3,104,226 years. To put that in perspective: the blast energy could power the entire United States for 3.27 days.[15]
3	The total energy of all explosives used in World War Two (including the Hiroshima and Nagasaki bombs) is estimated to have been 3 megatons of TNT.
8.6	The amount of energy released by a "average" tropical cyclone in 1 minute, mainly due to water condensation. Winds are a quarter of a percent of that amount.[16]
21.5	The maximum theoretical yield from 1 kg of matter by converting all of the mass into energy (by mass–energy equivalence, E = mc2) yields 89.8 petajoules or the equivalent of 21.5 megatons of TNT. No practical method of total conversion exists today, such as combining 500 grams of matter with 500 grams of antimatter. However, in the case of proton–antiproton annihilation, approximately 50% of the released energy will escape in the form of neutrinos, which are almost undetectable.[17] Electron–positron annihilation events emit their energy entirely as gamma rays.
25, 50, 100	During the Cold War, the United States developed hydrogen bombs with a maximum theoretical yield 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).[18] The actual destructive potential of such weapons can vary greatly depending on conditions, such as the altitude at which they are detonated, the nature of the target they are detonated against, and the physical features of the landscape where they are detonated.
26.3	Megathrust earthquakes 2004 Indian Ocean earthquake released record ME surface rupture energy, or potential for damage at 26.3 megatons of TNT (110 PJ). See total energy released 6 steps below.
540	The total amount of all nuclear testing and combat from 1945 to present is about 540 megatons.
7,000	The total global nuclear arsenal is about 30,000 nuclear warheads with a destructive capacity of 7,000 megatons or 7 gigatons (7,000 million tons) of TNT.
62,500	The amount of total solar energy input to the Earth per minute is 440 exajoules.
6,000,000 = 7006600000000000000♠6×106	The approximate energy released when the largest fragment of Comet Shoemaker–Levy 9 impacted Jupiter was estimated to be equal to 6 million megatons (or 6 trillion tons) of TNT.
7006932000000000000♠9.32×106	The amount of 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,[19] 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	Megathrust earthquakes record huge MW values, or total energy released. The 2004 Indian Ocean earthquake released 9,560 gigatons TNT equivalent.
7008100000000000000♠1×108	The approximate energy released when the Chicxulub impact caused the mass extinction 66 million years ago was estimated to be equal to 100 teratons (i.e. 100 exagrams or approximately 220.462 quadrillion pounds) of TNT. 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.
7015789000000000000♠7.89×1015	Total solar output in all directions per day.
7028239999999999999♠2.4×1028–7028479999999999999♠4.8×1028	On a much grander scale, a type 1a supernova explosion gives off 1–2x1044 joules of energy, which is about 2.4 to 4.8 hundred billion yottatons (24 to 48 octillion (2.4–4.8x1028) megatons) of TNT, equivalent to the explosive force of a quantity of TNT over a trillion (1012) times the mass of the planet Earth. The Type 1a supernova is essentially the fusion detonation of all the fusable fuel in a star of about 1.4 solar masses within a few seconds, and is a standard candle used for intergalactic distance measurements.
7030240000000000000♠2.4×1030–7030480000000000000♠4.8×1030	The largest supernova explosions witnessed, so-called Gamma-ray bursts (GRBs) released more than 1046 joules of energy.[20]

For more, see Orders of magnitude (energy).

See also

• Nuclear arms race
• Orders of magnitude (energy)
• Relative effectiveness factor
• Ton
• Tonne
• Tonne of oil equivalent, a unit of energy almost exactly 10 tonnes of TNT
• Table of explosive detonation velocities

References

1. ↑ "Tons (Explosives) to Gigajoules Conversion Calculator". unitconversion.org. 
2. ↑ "Joules to Megatons Conversion Calculator". unitconversion.org. 
3. ↑ Blast effects of external explosions (Section 4.8. Limitations of the TNT equivalent method)
4. ↑ "Appendix B8 – Factors for Units Listed Alphabetically".  In NIST SI Guide 2008
5. ↑ Cooper, Paul W. (1996). Explosives Engineering. New York: Wiley-VCH. p. 406. ISBN 0-471-18636-8. 
6. ↑ Muller, Richard A. (2001–2002). "Chapter 1. Energy, Power, and Explosions". Physics for Future Presidents, a textbook. ISBN 978-1-4266-2459-9. 
7. ↑ Sorin Bastea, Laurence E. Fried, Kurt R. Glaesemann, W. Michael Howard, P. Clark Souers, Peter A. Vitello, Cheetah 5.0 User's Manual, Lawrence Livermore National Laboratory, 2007.
8. ↑ Maienschein, Jon L. (2002). Estimating equivalency of explosives through a thermochemical approach (PDF) (Technical report). Lawrence Livermore National Laboratory. UCRL-JC-147683. 
9. ↑ 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. 
10. ↑ Cunningham, Bruce J. (2001). C-4/tnt equivalency (Technical report). Lawrence Livermore National Laboratory. EMPE-01-81. 
11. ↑ "Arc blast Tri-Nitro-Toluene TNT Trotyl equivalent - ARCAD INC.". arcblasts.com. 
12. ↑ "The Ingenuity Gap: Facing the Economic, Environmental, and Other Challenges", Thomas F. Homer-Dixon, p. 249.
13. ↑ TECH REPS INC ALBUQUERQUE NM (1986). "Minor Scale Event, Test Execution Report" (PDF). 
14. ↑ "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)
15. ↑ "Country Comparison :: Electricity – consumption". The World Factbook. CIA. Retrieved 2009-10-22.  (Calculated from 2007 value of 3,892,000,000,000 kWh annual usage)
16. ↑ "NOAA FAQ: How much energy does a hurricane release?". National Oceanic & Atmospheric Administration. August 2001. Retrieved 2009-06-30.  cites 6e14 watts continuous.
17. ↑ 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. 
18. ↑ See Currently deployed U.S. nuclear weapon yields, Complete List of All U.S. Nuclear Weapons, Tsar Bomba, all from Carey Sublette's Nuclear Weapon Archive.
19. ↑ "USGS.gov: USGS WPhase Moment Solution". Earthquake.usgs.gov. Archived from the original on 13 March 2011. Retrieved 13 March 2011. 
20. ↑ Maselli, A.; Melandri, A.; Nava, L.; Mundell, C. G.; Kawai, N.; Campana, S.; Covino, S.; Cummings, J. R.; Cusumano, G.; Evans, P. A.; Ghirlanda, G.; Ghisellini, G.; Guidorzi, C.; Kobayashi, S.; Kuin, P.; LaParola, V.; Mangano, V.; Oates, S.; Sakamoto, T.; Serino, M.; Virgili, F.; Zhang, B.- B.; Barthelmy, S.; Beardmore, A.; Bernardini, M. G.; Bersier, D.; Burrows, D.; Calderone, G.; Capalbi, M.; Chiang, J. (2013). "GRB 130427A: A Nearby Ordinary Monster". Science 343 (6166): 48–51. doi:10.1126/science.1242279. PMID 24263134. 

• 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.