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

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

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. In the SI system the above E_k will be in unit joule if the mass, m, is in kilogram, and the speed, v, is in metre per second.

Subsonic ammunition

A subsonic variant of ammunition that would otherwise be supersonic has its velocity limited to less than the speed of sound, i.e. v is fixed at around 300 metres per second (980 ft/s). For ammunition with this limitation the muzzle energy is variable only with respect to the bullet mass m.

Typical muzzle energies of common firearms and cartridges

Typical Muzzle Energies of Common Firearms and Cartridges

Caliber	Firearm	Bullet weight, g (gr)	Velocity, m/s (ft/s)	Muzzle energy, J (ft lb)
.22 Long Rifle	rifle, handgun	2.5 (38)	300 (1,000)	140 (100)
.380 ACP	handgun	5.8 (90)	300 (1,000)	270 (200)
.38 Special	handgun	7.5 (115)	270 (900)	300 (220)
9mm	handgun	7.5 (115)	370 (1,200)	540 (400)
.357	handgun	8.1 (125)	460 (1,500)	846 (624)
10mm	handgun	10.0 (155)	386 (1,265)	750 (550)
.40	handgun	7.5 (115)	360 (1,180)	649 (479)
.44 Magnum	handgun	12 (180)	470 (1,550)	1,150 (850)
.45 ACP	handgun	12.0 (185)	300 (970)	523 (386)
.45 Colt	handgun	14.6 (225)	240 (800)	340 (250)
5.45×39mm	AK-74 rifles	3.4 (53)	880 (2,900)	1,327 (979)
5.56×45mm NATO	M4, M16, AR-15 style rifles	4.0 (62)	991 (3,251)	1,767 (1,303)
7.62 mm	AK-47, M14 rifles	9.3 (144)	838 (2,749)	3,304 (2,437)
.308	rifle	9.7 (150)	860 (2,820)	3,590 (2,648)
.270 Winchester	rifle	9.7 (150)	880 (2,900)	3,798 (2,801)
.30-06	M1 Garand rifle	9.7 (150)	890 (2,920)	3,849 (2,839)
7mm Remington Magnum	rifle	10.7 (165)	900 (2,950)	4,330 (3,190)
.300 Winchester Magnum	rifle	12 (180)	900 (2,960)	4,700 (3,500)
.300 Weatherby Magnum	rifle	12 (180)	970 (3,190)	5,430 (4,005)
.375 H&H Magnum	rifle	19 (300)	860 (2,830)	5,783 (4,265)
.458 Winchester Magnum	rifle	26 (400)	752 (2,468)	7,336 (5,411)
.50 BMG	rifle	49 (750)	860 (2,820)	17,952 (13,241)
M829A3	anti-tank round	10,000 (150,000)	1,600 (5,100)	12,100,000 (8,900,000)

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. 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.

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. 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.

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

See also

• Free recoil
• Muzzle velocity
• Power factor (shooting sports)

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.