# Muzzle energy

Pellet exiting muzzle, with formula for energy overlaid.

Muzzle energy is the kinetic energy of a bullet as it is expelled from the muzzle of a firearm. Without consideration of factors such as aerodynamics and gravity for the sake of comparison, muzzle energy is used as a rough indication of the destructive potential of a given firearm or cartridge, the heavier the bullet and especially the faster it moves, the higher its muzzle energy and the more damage it will do.

## Kinetic energy

The general formula for the kinetic energy is

${\displaystyle E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}}$

where

v is the velocity of the bullet
m is the mass of the bullet.

Although both mass and velocity contribute to the muzzle energy, the muzzle energy is proportional to the mass while proportional to the square of the velocity, the velocity of the bullet is a more important determinant of muzzle energy. For a constant velocity, if the mass is doubled, the energy is doubled; however, for a constant mass, if the velocity is doubled, the muzzle energy increases four times.[1] In the SI system the above Ek will be in unit joule if the mass, m, is in kilogram, and the speed, v, is in metre per second.

## Typical muzzle energies of common firearms and cartridges

Typical Muzzle Energies of Common Firearms and Cartridges[1]
Caliber Firearm Bullet weight, g (gr) Velocity, m/s (ft/s) Muzzle energy, J (ft lb)
.22 Long Rifle rifle, handgun 2.5 (38)[1] 300 (1,000)[1] 140 (100)[1]
.22 Long Rifle HV rifle, handgun 2.33 (36) 400 (1310) 186 (137)
.32 ACP handgun 5 (73) 318 (1043) 240 (177)
.38 ACP handgun 8 (125) 340 (1100) 456 (336)
.380 ACP handgun 5.8 (90)[1] 300 (1,000)[1] 270 (200)[1]
.38 Special handgun 7.5 (115)[1] 270 (900)[1] 300 (220)[1]
9x19mm handgun 7.5 (115)[1] 370 (1,200)[1] 540 (400)[1]
.357 handgun 8.1 (125)[1] 460 (1,500)[1] 846 (624)[1]
10mm handgun 10.0 (155)[1] 386 (1,265)[1] 750 (550)[1]
.40 handgun 7.5 (115)[1] 360 (1,180)[1] 649 (479)[1]
.44 Magnum handgun 12 (180)[1] 470 (1,550)[1] 1,150 (850)[1]
.45 ACP handgun 12.0 (185)[1] 300 (970)[1] 523 (386)[1]
.45 Colt handgun 14.6 (225)[1] 240 (800)[1] 340 (250)[1]
5.45×39mm AK-74 rifles 3.4 (53)[1] 880 (2,900)[1] 1,327 (979)[1]
5.56×45mm NATO M4, M16, AR-15 style rifles 4.0 (62)[1] 991 (3,251)[1] 1,767 (1,303)[1]
7.62 mm AK-47, M14 rifles 9.3 (144)[1] 838 (2,749)[1] 3,304 (2,437)[1]
.308 rifle 9.7 (150)[1] 860 (2,820)[1] 3,590 (2,648)[1]
.270 Winchester rifle 9.7 (150)[1] 880 (2,900)[1] 3,798 (2,801)[1]
.30-06 M1 Garand rifle 9.7 (150)[1] 890 (2,920)[1] 3,849 (2,839)[1]
7mm rifle 10.7 (165)[1] 900 (2,950)[1] 4,330 (3,190)[1]
.300 Winchester Magnum rifle 12 (180)[1] 900 (2,960)[1] 4,700 (3,500)[1]
.300 Weatherby Magnum rifle 12 (180)[1] 970 (3,190)[1] 5,430 (4,005)[1]
.375 H&H Magnum rifle 19 (300)[1] 860 (2,830)[1] 5,783 (4,265)[1]
.458 Winchester Magnum rifle 26 (400)[citation needed] 730 (2,380)[1] 6,820 (5,030)[1]
.50 BMG rifle 49 (750)[citation needed] 860 (2,820)[citation needed] 17,952 (13,241)[citation needed]
M829A3 anti-tank round 10,000 (150,000)[citation needed] 1,600 (5,100)[citation needed] 12,100,000 (8,900,000)[citation needed]

It must be stressed that muzzle energy is dependent upon the factors previously listed and that even velocity is highly variable depending upon the length of the barrel a projectile is fired from.[2] Also note that the muzzle energy is only an upper limit for how much energy is transmitted to the target and that the effects of a ballistic trauma depend on several other factors as well. While the above list mentions some averages, there is wide variation in commercial ammunition. A 180 grain bullet fired from .357 magnum handgun can achieve a muzzle energy of 580 foot-pounds. A 110 grain bullet fired from the same gun might only achieve 400 foot-pounds of muzzle energy, depending upon the manufacture of the cartridge, some .45 Colt ammunition can produce 1,200 foot-pounds of muzzle energy, far in excess of the average listed above.[citation needed]

## Legal requirements on muzzle energy

Some jurisdictions stipulate minimum muzzle energies for hunting, for example, in Denmark rifle ammunition used for hunting the largest types of game there such as red deer must 100 m down range have a kinetic energy E100 of at least 2700 J and a bullet mass of at least 9 g or alternatively an E100 of at least 2000 J and a bullet mass of at least 10 g.[3] Namibia specifies three levels of minimum muzzle energy for hunting, 1350 J for game such as springbok, 2700 J for game such as hartebeest and 5400 J for big game, together with a minimum caliber of 7 mm.[4]

In Germany airsoft guns with a muzzle energy of no more than 0.5 J are exempt from the gun law,[5] while air guns with a muzzle energy of no more than 7.5 J may be acquired without a firearms license.[6]

## Resources

• Edward F. Obert, Thermodynamics, McGraw-Hill Book Co., 1948.
• Mc Graw-Hill encyclopedia of Science and Technology, volume ebe-eye and ice-lev, 9th Edition, Mc Graw-Hill, 2002.

## References

1. Rhee, Peter M.; Moore, Ernest E.; Joseph, Bellal; Tang, Andrew; Pandit, Viraj; Vercruysse, Gary (2016-06-01). "Gunshot wounds: A review of ballistics, bullets, weapons, and myths". The Journal of Trauma and Acute Care Surgery. 80 (6): 853–867. doi:10.1097/TA.0000000000001037. ISSN 2163-0755. PMID 26982703.
2. ^ "BBTI - Ballistics by the Inch - Home". ballisticsbytheinch.com.[better source needed]
3. ^ "Bekendtgørelse om skydevåben og ammunition, der må anvendes til jagt m.v." [Hunting weapons and ammunition act]. retsinformation.dk (in Danish). Miljøministeriet. 2012-12-17. Ammunition. Retrieved 2015-03-10.
4. ^ "NAPHA - Namibia Professional Hunting Assiation: Hunting Laws& Rifle Importation". napha-namibia.com. Retrieved 5 July 2015.
5. ^ "Ab welcher Geschossenergie fallen Soft-Air-Waffen unter das Waffengesetz?" [From which muzzle energy does Airsoft guns fall under the gun law?]. www.bmi.bund.de (in German). Retrieved 2015-09-17.
6. ^ "Waffengesetz (WaffG)" [gun law]. gesetze-im-internet.de (in German). Retrieved 2015-09-19.