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 speed of the bullet and

m is the mass of the bullet.

Calculating muzzle energy

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

None of the units on this page is correct. The foot pound is not a unit of energy (pounds feet squared per second squared is the relevant unit of eneregy). Neither is it a unit of force. There appears to be some confusion between lb.f (pound foot) and lbf (pound force). Likewise, considerable reference is made here to the acceleration due to gravity. This is a purely local phenomenon and has no bearing whatever on the energy of a bullet fired from a gun, which would be identical on the surface of Jupiter or in deep space.

• 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. Most sporting arms publications within the United States report muzzle energies in foot-pound force. These units are not self-consistent thus a conversion factor must be added. The above formula thus becomes

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

• 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. 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

Typical muzzle energy levels of different types of firearms

Firearm	Caliber	Muzzle energy
		Foot-pounds	Joules
air gun	.177	15	20
rifle	.22LR	100	135
rifle	5.56 × 45 mm	1200	1550
pistol (semi-auto)	9 mm	350	540

Average muzzle energies for common pistol cartridges

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