**Gun Recoil Force Calculator**

Enter the values of mass, m_{(lbs)}, velocity, V_{(ft/s)} and recoil distance, RD_{(in)} to determine the value of gun recoil force, GRF_{(lbf)}.

**Gun Recoil Force Formula**

The gun recoil force is calculated to determine the backward momentum experienced by a shooter when a firearm is discharged. This force is a result of the conservation of momentum, where the forward motion of the bullet generates an equal and opposite reaction that pushes the gun backwards.

Gun recoil force, GRF_{(lbf)} in pounds-force by taking the product of the mass, m_{(lbs)} in pounds and the square of the velocity, V_{(ft/s)} in feet per second and then dividing by the product of the recoil distance, RD_{(in)} in inches and the gravitational constant in metres per second squared(32.174049m/s^{2}).

Gun recoil force, GRF_{(lbf)} = m_{(lbs)} * V^{2}_{(ft/s)} / (RD_{(in)} / 12) * 32.174049

GRF_{(lbf)} = gun recoil force in pounds-force, lbf.

m_{(lbs)} = mass in pounds, lbs.

V_{(ft/s)} = velocity in feet per seconds, ft/s.

RD_{(in)} = recoil distance in inches, in.

__Gun Recoil Force Calculation:__

- A bullet with a mass of 0.4 pounds is fired at a velocity of 2800 feet per second. The recoil is absorbed over a distance of 1 inch by the gun’s mechanisms.

Given: m_{(lbs)} = 0.4lbs, V_{(ft/s)} = 2800ft/s, RD_{(in)} = 1in.

Gun recoil force, GRF_{(lbf)} = m_{(lbs)} * V^{2}_{(ft/s)} / (RD_{(in)} / 12) * 32.174049

GRF_{(lbf)} = 0.4 * 2800^{2} / (1/12) * 32.174049

GRF_{(lbf)} = 3136000 / 2.681587

GRF_{(lbf)} = 1169.24lbf.

- A gun recoil force of 50 pounds-force is fired at a velocity of 2500 feet per second. The recoil is absorbed over a distance of 6 inch by the gun’s mechanisms.

Given: GRF_{(lbf)} = 50lbf, V_{(ft/s)} = 2500ft/s, RD_{(in)} = 6in.

Gun recoil force, GRF_{(lbf)} = m_{(lbs)} * V^{2}_{(ft/s)} / (RD_{(in)} / 12) * 32.174049

m_{(lbs)} = GRF_{(lbf)} * (RD_{(in)} / 12) * 32.174049 / V^{2}_{(ft/s)}

m_{(lbs)} = 50 * (6/12) * 32.174049 / 2500^{2}

m_{(lbs)} = 804.351225 / 6250000

m_{(lbs)} = 0.1287lbs.