# TNT equivalent

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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 (or tonne) of TNT is a unit of energy equal to 4.184 gigajoules, which is approximately the amount of energy released in the detonation of one ton of TNT. The megaton is a unit of energy equal to 4.184 petajoules.[1]

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). 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 more than 60% more energy density (approximately 7.5 MJ/kg, compared to 4.7 MJ/kg for TNT).

## Value

A gram of TNT releases 4100–4602 Joules upon explosion. To define the tonne of TNT, this was arbitrarily standardized by letting 1 gram TNT = 4184 J (exactly).[2]

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.[3]

The measured pure heat output of a gram of TNT is only 2724 J,[4] but this is not the important value for explosive blast effect calculations.

A kiloton of TNT can be visualized as a cube of TNT of 8.46 metres on a side.

Grams TNT Symbol Tons TNT Symbol Energy
gram of TNT g microton of TNT μt 4.184×103 J
kilogram of TNT kg milliton of TNT mt 4.184×106 J
megagram of TNT Mg ton of TNT t 4.184×109 J
gigagram of TNT Gg kiloton of TNT kt 4.184×1012 J
teragram of TNT Tg megaton of TNT Mt 4.184×1015 J
petagram of TNT Pg gigaton of TNT Gt 4.184×1018 J

## Examples

• Conventional bombs yield range from less than 1 ton to MOAB's 11 tonnes.
• Minor Scale, a 1985 United States conventional explosion utilizing 4,400 tonnes of ANFO explosive to simulate a 4 kilotons of TNT (17 TJ) nuclear explosion, is believed to be the largest planned detonation of conventional explosives in history.
• The Little Boy atomic bomb dropped on Hiroshima on August 6, 1945, exploded with an energy of about 15 kilotons of TNT (63 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.
• 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).[5] 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.
• The energy contained in 1 megaton of TNT (4.2 PJ) is enough power the average American household (in the year 2007) for 103,474 years.[6] 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.[7]
• The total global nuclear arsenal is about 30,000 nuclear warheads with a destructive capacity of 5,000 megatons or 5 gigatons (5,000 million tons) of TNT.
• Megathrust earthquakes record huge MW values, or total energy released. The 2004 Indian Ocean Earthquake released 9,560 gigatons of TNT (40,000 EJ) equivalent, but its ME (surface rupture energy, or potential for damage) was far smaller at 26.3 megatons of TNT (110 PJ).
• On a much grander scale, supernova explosions give off about 1044 joules of energy, which is about ten octillion (1028) megatons of TNT.
• 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.
• The maximum theoretical yield from 1 kg of matter would be produced by annihilating it with an equal amount of antimatter, converting all of the mass into energy.[8] According to mass-energy equivalence, this reaction would produce a total of 2 × 8.99 ×1016 J, which is equal to 42.96 Mt.

## References

1. ^ Joules to Megatons Conversion Calculator
2. ^ NIST Guide for the Use of the International System of Units (SI): Appendix B8—Factors for Units Listed Alphabetically
3. ^ Cooper, Paul. Explosives Engineering, New York: Wiley-VCH, 1996, p. 406.
4. ^ "Physics for Future Presidents, a textbook", 2001–2002, Richard A. Muller, Chapter 1. Energy, Power, and Explosions
5. ^ 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.
6. ^ "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)
7. ^ "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)
8. ^ In antiproton annihilation, about 50% of this energy is carried off by effectively invisible neutrinos (see S.K. Borowski,Comparison of Fusion/Antiproton Propulsion systems); in contrast, almost 100% of electron-positron annihilation events emit their energy entirely as gamma rays.

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