Recoil Energy Calculator — Free Recoil & Velocity
When a bullet leaves a barrel, Newton's third law forces the firearm to recoil with equal and opposite momentum. Enter the projectile mass, muzzle velocity and firearm mass to calculate the free recoil energy, recoil velocity and impulse.
g
m/s
kg
Kinetic energy imparted to the firearm by the recoil impulse
- 1
Bullet mass in kg
9.5 g ÷ 1000 = 0.0095 - 2
Recoil momentum
0.0095 × 370 m/s = 3.515By conservation of momentum, gun momentum equals bullet momentum. - 3
Recoil velocity
3.515 ÷ 0.9 kg = 3.9056 - 4
Free recoil energy
½ × 0.9 × 3.9056² = 6.86
How does this calculator work?
Free recoil energy = ½ × m_gun × (m_bullet × v_bullet / m_gun)². Conservation of momentum means the gun's recoil momentum equals the bullet's forward momentum. Heavier firearms reduce recoil velocity and energy for the same cartridge; heavier bullets increase recoil linearly.
Formula
How this is calculated
When a firearm discharges, the system (gun + bullet) is in approximate momentum equilibrium before the shot. By conservation of momentum, the momentum of the bullet leaving the barrel (m_bullet × v_bullet) must equal the recoil momentum gained by the gun (m_gun × v_recoil). Rearranging gives the free recoil velocity: v_recoil = (m_bullet × v_bullet) / m_gun.
Free recoil energy is the kinetic energy imparted to the firearm: E = ½ · m_gun · v_recoil². Because the gun is much heavier than the bullet, the recoil velocity is much lower than the muzzle velocity — but the energy ratio is proportionally smaller still, since energy scales with v². Typical free recoil energies range from about 1–2 J for .22 LR cartridges to 60 J or more for large rifle calibres.
This model uses simplified free recoil (the gun is treated as a free particle, ignoring propellant gas mass and the shooter's grip). Real felt recoil is also affected by the stock shape, recoil pad, and recoil management system of the firearm. Enter the unloaded firearm mass (excluding magazine and ammunition) for a realistic result.
Frequently asked questions
Free recoil is the theoretical kinetic energy the firearm receives, calculated purely from conservation of momentum. Felt recoil is the subjective sensation, which is affected by the shooter's grip, stock geometry, recoil pads, and recoil-operated mechanisms that spread the impulse over a longer time.
Momentum (m × v) is conserved and equals the bullet's momentum regardless of gun mass. But a heavier gun reaches a lower recoil velocity for the same momentum, so its kinetic energy (½mv²) is also lower — making heavier guns objectively gentler to shoot.
Both contribute equally to recoil momentum (m × v). However, a heavier bullet at the same momentum produces less muzzle energy than a lighter, faster bullet — so reducing bullet mass and boosting velocity increases muzzle energy while keeping recoil similar.
Also known as
TG we-Calculate Editorial Team. (2026). Recoil Energy Calculator — Free Recoil & Velocity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/recoil-energy-calculator
TG we-Calculate Editorial Team. "Recoil Energy Calculator — Free Recoil & Velocity." TG we-Calculate. 2026. https://we-calculate.com/calculator/recoil-energy-calculator.
TG we-Calculate Editorial Team, "Recoil Energy Calculator — Free Recoil & Velocity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/recoil-energy-calculator
@misc{wecalculate_recoil_energy_calculator, title = {Recoil Energy Calculator — Free Recoil & Velocity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/recoil-energy-calculator}}, year = {2026}, note = {TG we-Calculate} }
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