Gun Recoil Momentum Calculator

Firearm recoil: m_gun·v_gun = m_proj·v_proj

Recoil comes straight out of conservation of linear momentum. Before the shot the total is zero; after it, the projectile's forward momentum matches the firearm's rearward momentum. m_gun·v_gun = m_proj·v_proj. Propellant gases tack on a secondary impulse, usually 1.5–1.75× the projectile term. Take a 1 kg pistol firing an 8 g bullet at 360 m/s: it recoils at roughly v_gun = (0.008·360)/1 ≈ 2.9 m/s. A .50 BMG rifle puts out around 14 J of free recoil energy, which lands as a hard shove on the shoulder.

Applications

Ergonomic stock and grip design spreads recoil across the shoulder pocket so the muzzle doesn't climb as much. When picking a cartridge for hunting or sport, you're weighing stopping power against how much recoil you can take. Muzzle brakes and gas-operated actions redirect propellant flow to trim the felt recoil. The same equation also runs rocket propulsion and artillery recoil systems.

FAQ

Why does a heavier gun recoil less? The projectile fixes the momentum, so a larger m_gun has to mean a smaller v_gun. And since recoil energy scales with v_gun² / 2, that smaller velocity counts double.

Does the shooter add to gun mass? In effect, yes. A firm shoulder mount couples in your body mass, which drops the effective recoil velocity and the force you feel.

What about propellant gas? The hot gases leaving the muzzle carry momentum of their own. To get the free-recoil energy right, engineering models add an ejecta term (m_gas·v_gas).