Gun Recoil Force Calculator, Formula, GRC Calculation

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/s²).

Gun recoil force, GRF_(lbf) =  m_(lbs) * V²_(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:

1. 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) * V²_(ft/s) / (RD_(in) / 12) * 32.174049

GRF_(lbf) = 0.4 * 2800² / (1/12) * 32.174049

GRF_(lbf) = 3136000 / 2.681587

GRF_(lbf) = 1169.24lbf.

2. 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) * V²_(ft/s) / (RD_(in) / 12) * 32.174049

m_(lbs) = GRF_(lbf) * (RD_(in) / 12) * 32.174049 / V²_(ft/s)

m_(lbs) = 50 * (6/12) * 32.174049 / 2500²

m_(lbs) = 804.351225 / 6250000

m_(lbs) = 0.1287lbs.

RECOIL OF A GUN