A list of variables are at the bottom of this page.

Recoil Velocity

The forward momentum (sometimes written as impulse), that of the bullet and powder charge are given by


Because momentum is conserved, this is equal to the rearward momentum of the firearm:


We can set these two equations equal to each other and solve for the velocity of the firearm, yielding


Recoil Energy

Once the velocity is found, the recoil energy can be found by solving

EF = 1/2 MF VF2


Assume a seven pound rifle using 40 grains of powder to shoot a 168 grain bullet at 2700 feet/sec. First find the mass of the bullet, charge and rifle

MB = 168 gr/(32.2 f/s2*7000 gr/lb) = 0.000745 slugs (unit of mass)
MC = 40 gr/(32.2 f/s2*7000 gr/lb) = 0.000177 slugs
MF = 7 lb/(32.2 f/s2) = 0.217 slugs

The constant 32.2 is the acceleration due to gravity, g, and is used to convert weight to mass:

Mass = Weight/g

The free recoil velocity can now be found

VF = (0.000745 slugs * 2700 f/s + 0.000177 slugs * 4700 f/s)/(0.217 slugs) = 13.1 f/s

And the free recoil energy is given by

EF = 0.5 * 0.217 slugs * (13.1 f/s)2 = 18.6 ft•lbs


MB Bullet mass VB Bullet velocity
MC Charge mass VC Charge velocity
MF Firearm mass VF Firearm velocity
EF Firearm energy g Acceleration due to gravity