Muzzle energy
Muzzle energy is the kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...

 of a bullet
A bullet is a projectile propelled by a firearm, sling, or air gun. Bullets do not normally contain explosives, but damage the intended target by impact and penetration...

 as it is expelled from the muzzle
Muzzle (firearm)
The muzzle of a firearm is the end of the barrel from which the projectile will exit.Precise machining of the muzzle is crucial to accuracy, because it is the last point of contact between the barrel and the projectile...

 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
v is the velocity
In physics, velocity is speed in a given direction. Speed describes only how fast an object is moving, whereas velocity gives both the speed and direction of the object's motion. To have a constant velocity, an object must have a constant speed and motion in a constant direction. Constant ...

 of the bullet
m is the mass
Mass can be defined as a quantitive measure of the resistance an object has to change in its velocity.In physics, mass commonly refers to any of the following three properties of matter, which have been shown experimentally to be equivalent:...

 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 kilogram
      The kilogram or kilogramme , also known as the kilo, is the base unit of mass in the International System of Units and is defined as being equal to the mass of the International Prototype Kilogram , which is almost exactly equal to the mass of one liter of water...

      s and the speed, v, is in metres per second
      Metre per second
      Metre per second is an SI derived unit of both speed and velocity , defined by distance in metres divided by time in seconds....

      , the calculated muzzle energy, Ek, will be in joule
      The joule ; symbol J) is a derived unit of energy or work in the International System of Units. It is equal to the energy expended in applying a force of one newton through a distance of one metre , or in passing an electric current of one ampere through a resistance of one ohm for one second...

    • If the mass, m, is in grams and the speed, v, is in kilometres per second, the calculated muzzle energy, Ek, will be in kilojoules.
  • In American engineering units:
  • Mass, m, is usually given in grains
    Grain (measure)
    A grain is a unit of measurement of mass that is nominally based upon the mass of a single seed of a cereal. From the Bronze Age into the Renaissance the average masses of wheat and barley grains were part of the legal definition of units of mass. However, there is no evidence of any country ever...

     and the speed, v, in feet per second but kinetic energy, Ek, is typically given in foot-pound force
    Foot-pound force
    The foot-pound force, or simply foot-pound is a unit of work or energy in the Engineering and Gravitational Systems in United States customary and Imperial units of measure. It is the energy transferred on applying a force of 1 pound-force through a displacement of 1 foot...

     (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:

  • When publishing kinetic energy tables for small arms ammunition, an acceleration due to gravity
    Standard gravity
    Standard gravity, or standard acceleration due to free fall, usually denoted by g0 or gn, is the nominal acceleration of an object in a vacuum near the surface of the Earth. It is defined as precisely , or about...

     of 32.163 ft/s2 rather than the standard of 32.1739 ft/s2 is used. The formula therefore becomes

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 .177 15 20
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
heavy .50 BMG 11,091 15,037
heavy 14.5 × 114 mm 23,744 32,000

Average muzzle energies for common pistol cartridges
Cartridge Muzzle energy
ft-lbf joules
.380 ACP
.380 ACP
The .380 ACP pistol cartridge is a rimless, straight-walled pistol cartridge developed by firearms designer John Browning. The cartridge headspaces on the mouth of the case. It was introduced in 1908 by Colt, and has been a popular self-defense cartridge ever since...

.38 Special
.38 Special
The .38 Smith & Wesson Special is a rimmed, centerfire cartridge designed by Smith & Wesson. It is most commonly used in revolvers, although some semi-automatic pistols and carbines also use this round...

9 mm Luger
9 mm Luger Parabellum
The 9×19mm Parabellum cartridge was designed by Georg Luger and introduced in 1902 by the German weapons manufacturer Deutsche Waffen- und Munitionsfabriken for their Luger semi-automatic pistol...

.45 Colt
.45 Colt
The .45 Colt cartridge is a handgun cartridge dating to 1872. It began as a black powder revolver round developed for the Colt Single Action Army revolver, but is offered as a magnum level handgun hunting round in modern usage. This cartridge was adopted by the U.S. Army in 1873 and served as the...

.45 GAP
.45 GAP
The .45 G.A.P. pistol cartridge was designed by Ernest Durham, an engineer with CCI/Speer, at the request of firearms manufacturer Glock to provide a cartridge that would equal the power of the .45 ACP but was shorter to fit in a more compact handgun, and with a stronger case head to reduce the...

.45 ACP
.45 ACP
The .45 ACP , also known as the .45 Auto by C.I.P., is a cartridge designed by John Browning in 1904, for use in his prototype Colt semi-automatic .45 pistol and eventually the M1911 pistol adopted by the United States Army in 1911.-Design and history:The U.S...

.40 S&W
.40 S&W
The .40 S&W is a rimless pistol cartridge developed jointly by major American firearms manufacturers Winchester and Smith & Wesson. The .40 S&W was developed from the ground up as a law enforcement cartridge designed to duplicate performance of the FBI's reduced velocity 10mm cartridge which could...

.357 Sig
.357 SIG
The .357 SIG pistol cartridge is the product of Swiss-German firearms manufacturer SIG-Sauer, in cooperation with the American ammunition manufacturer Federal Cartridge. While it is based on a .40 S&W case necked down to accept bullets, the .357 SIG brass is slightly longer...

.357 Mag 550745.7
10mm Auto 650881.3
.44 Mag 10001,355.8
.50 AE 15002,033.7
.454 Casull
.454 Casull
The .454 Casull is a firearm cartridge, developed in 1957 by Dick Casull and Jack Fulmer. It was first announced in November 1959 by Guns & Ammo magazine. The basic design was a lengthened and structurally improved .45 Colt case...

.460 SW 24003,254
.500 SW 26003,525.1

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.


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
    Muzzle velocity
    Muzzle velocity is the speed a projectile has at the moment it leaves the muzzle of the gun. Muzzle velocities range from approximately to in black powder muskets , to more than in modern rifles with high-performance cartridges such as the .220 Swift and .204 Ruger, all the way to for tank guns...

  • firearm
    A firearm is a weapon that launches one, or many, projectile at high velocity through confined burning of a propellant. This subsonic burning process is technically known as deflagration, as opposed to supersonic combustion known as a detonation. In older firearms, the propellant was typically...

  • foot-pound force
    Foot-pound force
    The foot-pound force, or simply foot-pound is a unit of work or energy in the Engineering and Gravitational Systems in United States customary and Imperial units of measure. It is the energy transferred on applying a force of 1 pound-force through a displacement of 1 foot...

  • free recoil
    Free recoil
    This article is about the energy produced by small arms when discharged. For other uses, go to Recoil Free recoil is a vernacular term or jargon for recoil energy...

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