Muzzle energy

Muzzle energy is the kinetic energy of a bullet as it is expelled from the muzzle of a firearm. It is often used as a rough indication of the destructive potential of a given firearm or load. The heavier the bullet and the faster it moves, the higher its muzzle energy and the more damage it will do. 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.

Calculating muzzle energy

Care must be taken when using this formula that consistent units are used.

• In SI units:
  • If the mass, m, is in kilograms and the speed, v, is in metres per second, the calculated muzzle energy, E_k, will be in joules.
  • If the mass, m, is in grams and the speed, v, is in kilometres per second, the calculated muzzle energy, E_k, will be in kilojoules.
• In American engineering units:

• Mass, m, is usually given in grains and the speed, v, in feet per second but kinetic energy, E_k, is typically given in foot-pound force (abbreviated ft-lbf). Most sporting arms publications within the United States report muzzle energies in foot-pound force. If m is specified in grains and v in feet per second, the following equation can be used, which gives the energy in foot-pound force:

$E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\times \left({\frac {1{\mbox{ ft}}\cdot {\mbox{lbf}}}{7000{\mbox{ gr}}\times 32.1739{\mbox{ ft}}^{2}{\mbox{/s}}^{2}}}\right)$

• When publishing kinetic energy tables for small arms ammunition, an acceleration due to gravity of 32.163 ft/s² rather than the standard of 32.1739 ft/s² is used^{[citation needed]}. The formula therefore becomes

$E_{k}={\begin{matrix}{\frac {1}{2}}\end{matrix}}mv^{2}\times \left({\frac {1{\mbox{ ft}}\cdot {\mbox{lbf}}}{7000{\mbox{ gr}}\times 32.163{\mbox{ ft}}^{2}{\mbox{/s}}^{2}}}\right)$

The bullet energy, remaining energy, down range energy and impact energy of a projectile may also be calculated using the above equations.

Typical muzzle energies of common firearms and cartridges

Example muzzle energy levels of different types of firearms

Firearm	Caliber	Muzzle energy
		ft-lbf	joules
air gun spring	.177	15	20
air gun mag spring	.22	22	30
air gun PCP	.22	30+	40+
pistol	.22LR	117	159
pistol	9 mm	383	519
pistol	.45 ACP	416	564
rifle	5.56 × 45 mm	1,325	1,796
rifle	7.62 × 39 mm	1,527	2,070
rifle	7.62 × 51 mm	2,802	3,799

Average muzzle energies for common pistol cartridges

Cartridge	Muzzle energy
	ft-lbf	joules
.380 ACP	199	270
.38 Special	310	420
9 mm Luger	350	470
.45 Colt	370	500
.45 GAP	400	540
.45 ACP	400	540
.40 S&W	425	576
.357 Sig	475	644
.357 Mag	550	750
10mm Auto	650	880
.44 Mag	1,000	1,400
.50 AE	1,500	2,000
.454 Casull	1,900	2,600
.460 SW	2,400	3,300
.500 SW	2,600	3,500

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 does not necessarily reflect how much energy is transmitted to the target. 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.

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.

See also

• muzzle velocity
• firearm
• foot-pound force
• free recoil