Recoil energy is the measured energy in translational kinetic energy (Et) imparted to the shooter of a firearm when discharged and is expressed in Joule (J) or Foot-pound force (ft-lbf).

Recoil energy, sometimes called “free recoil”, is a byproduct of the propulsive force from the powder charge held within a firearm chamber or breech. The physical event of recoil energy occurs when a powder charge is detonated within a firearm, resulting in the conversion of its chemical energy to thermodynamic energy. This energy is then transferred to the base of the projectile and to the rear of the cartridge or breech, recoiling the firearm rearward into the shooter while the projectile is propelled forward down the barrel. The rearward energy of the firearm when calculated is the recoil energy and the forward energy of the projectile when calculated and is the muzzle energy.

The concept or word usage of free recoil comes from the tolerability of gross recoil energy. Trying to figure the net recoil energy of a firearm (also known as felt recoil) is a futile endeavor. Even if you can calculate the recoil energy loss due to: muzzle brake; recoil operated action or gas operated action; mercury recoil suppression tube; recoil reducing butt pad and or hand grip; shooting vest and or gloves, the human factor is not calculable.

Therefore, free recoil stands as a scientific measurement of recoil energy, just as room temperature is measured. The comfort level of a shooter’s ability to tolerate free recoil is a personal perception. Just as it is a personal perception of how comfortable he or she feels to room temperature.

There are many factors that determine how a shooter will perceive the recoil energy of his or her small arm. Some of the factors are, but not limited to: body mass; body frame; experience; shooting position; recoil suppression equipment; small arm fit and or environmental stressors.

## Calculating recoil energy

There are several different ways to calculate recoil energy. However, the most common is the momentum long form and momentum short. Both equations yield a recoil energy in Joules (J) for SI or metric units of measure or Foot-pound force (ft-lbf) for English units of measure. Typically there is a conversion factor of 1000 or 7000 inserted into the equations to set the equation correct for kilograms and pounds. The reason for the conversion factors is that most people use these equations for the calculation of small arms when bullet weights are in grams and grains.

### In SI (metric) units of measure

Momentum long from: Gun velocity = (bullet mass x bullet velocity) + (powder charge mass x powder charge velocity) / Gun mass x 1000. Then, plug the now known Gun velocity into the translational kinetic energy formula: Recoil energy = 0.5 x Gun mass x Gun velocity2.

Example:

Firearm: Mauser 98 chambered in 7 x 57 mm Mauser weighing 4.54 kilograms.
Projectile: spitzer type bullet weighing 9.1 grams with a muzzle velocity of 823 meters per second.
Powder charge: single base nitrocellulose weighing 2.75 grams with a powder charge velocity of 1585 meters per second.
• 2.61 m/s = (9.1 x 823) + (2.75 x 1585) / 4.54 x 1000.

Then, plug the now known Gun velocity of 2.61 meters per second into the translational kinetic energy formula:

• 15.43 J = 0.5 x 4.54 x 2.612.

Momentum short form: Recoil energy = 0.5 x {[ (bullet mass x bullet velocity) + (powder charge mass x powder charge velocity) / 1000]2} / Gun mass.

Example, same as above:

• 15.43 J = 0.5 x {[ (9.1 x 823) + (2.75 x 1585) / 1000]2} / 4.54.

### In English units of measure

Momentum long from: Gun velocity = (bullet mass x bullet velocity) + (powder charge mass x powder charge velocity) / Gun mass x 7000. Then, plug the now known Gun velocity into the translational kinetic energy formula: Recoil energy = Gun mass x Gun velocity2 / 2 x dimensional constant.

Example:

Firearm: Mauser 98 chambered in 7 x 57 mm Mauser weighing 10 pounds.
Projectile: spitzer type bullet weighing 140 grains with a muzzle velocity of 2700 feet per second.
Powder charge: single base nitrocellulose weighing 42.5 grains with a powder charge velocity of 5200 feet per second.
• 8.557 ft/s = (140 x 2700) + (42.5 x 5200) / 10 x 7000.

Then, plug the now known Gun velocity of 8.557 feet per second into the translational kinetic energy formula:

• 11.38 ft-lbf = 10 x 8.5572/ 2 x 32.163.

Momentum short form: Recoil energy = {[ (bullet mass x bullet velocity) + (powder charge mass x powder charge velocity) / 7000]2} / Gun mass x 2 x dimensional constant.

Example, same as above:

• 11.38 ft-lbf = {[ (140 x 2700) + (42.5 x 5200) / 7000]2} / 10 x 2 x 32.163.

#### Powder Charge Velocities

Typically the charge velocity are:

Black powder: 685.8 m/s (2250 ft/s)
Pistol and Shotgun powder: 1707 m/s (5600 ft/s)
Rifle powder: 1585 m/s (5200 ft/s)
BMG powder: 1433 m/s (4700 ft/s)

However these charge velocities are approximations.