What formula is used for recoil velocity?

The formula derives from conservation of linear momentum: p_before = p_after. Since both gun and projectile start at rest, total momentum is zero. Therefore: m_gun × v_recoil = m_projectile × v_muzzle, which gives v_recoil = (m_projectile × v_muzzle) / m_gun.

Does this account for propellant gas mass?

No. This calculator uses the simplified two-body model (bullet + gun). For a more precise estimate of free-recoil velocity, add roughly half the propellant charge mass to the projectile mass. The tool still gives a close approximation for most practical comparisons.

What is the difference between recoil velocity and recoil energy?

Recoil velocity is how fast the firearm moves rearward immediately after firing. Recoil energy (free-recoil energy) is the kinetic energy of that rearward motion: KE = 0.5 × m_gun × v_recoil². Higher recoil energy is what the shooter feels as "kick."

Why does a heavier gun have less recoil velocity?

Momentum must be conserved. For a fixed bullet mass and muzzle velocity the total recoil momentum is constant. Distributing that same momentum over a larger gun mass means the gun moves at a slower velocity — v = p / m.

Can I use this for non-firearm systems?

Yes. The same physics applies to any reaction system where one mass is ejected from another — rockets, pneumatic launchers, paintball markers, or compressed-air cannons. Just enter the ejected-mass, ejection velocity, and body mass.

Recoil Velocity Calculator

Enter projectile mass, projectile velocity, and gun mass to instantly compute recoil velocity in metric or imperial units.

Recoil Parameters

Unit System

Metric (kg / m/s) Imperial (lb / ft/s)

Projectile Mass (kg)

Muzzle Velocity (m/s)

m/s

Firearm Mass (kg)

Formula

v_recoil = (m_projectile × v_muzzle) / m_gun

Derived from conservation of linear momentum: the total momentum before firing (zero, system at rest) equals the total momentum after firing.

Enter values and click Calculate to see recoil velocity

Summary

This calculator applies conservation of linear momentum to find the recoil velocity of a firearm or any two-body system. When a projectile is fired, momentum is conserved: the forward momentum of the bullet equals the rearward momentum of the gun. Enter the projectile mass, muzzle velocity, and gun mass and the tool returns the recoil velocity instantly, entirely in your browser.

How it works

Select your preferred unit system: metric (kg / m/s) or imperial (lb / ft/s).
Enter the projectile (bullet) mass in the selected unit.
Enter the muzzle velocity — the speed the projectile leaves the barrel.
Enter the firearm (gun) mass.
Click "Calculate" to see the recoil velocity, recoil momentum, and recoil energy.
Use the Reset button to clear all inputs and start over.

Use cases

Estimate the felt recoil of a rifle or handgun before purchasing.
Compare recoil across different cartridges for the same firearm.
Solve physics homework problems on conservation of momentum.
Analyze recoil forces in mechanical or pneumatic launch systems.
Design muzzle brakes or suppressors by quantifying baseline recoil momentum.
Study how gun mass affects recoil velocity for a fixed cartridge.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu