Recoil Velocity Calculator

This calculator uses conservation of linear momentum for a free-recoiling system.

• p = m_proj v_proj + m_gas v_gas
• v_recoil = p / m_gun
• E_recoil = ½ m_gun v_recoil²
• F̄ ≈ p / Δt (if impulse time is provided)

1. Enter gun mass, projectile mass, and projectile velocity.
2. Add propellant gas mass for a fuller estimate.
3. Pick a gas method: factor or direct velocity.
4. Optionally enter impulse time to estimate average force.
5. Press Calculate to view results above the form.
6. Use CSV or PDF buttons to export results.

Sample inputs and approximate recoil speeds for testing.

Recoil Velocity Guide

1) Why recoil velocity matters

Recoil velocity estimates the firearm’s backward speed after discharge. It supports comparisons when changing gun mass, muzzle velocity, or load choice. Many shoulder-fired setups fall near 1–6 m/s in free recoil, while heavier platforms can be lower.

2) Momentum model behind the calculator

The calculator applies conservation of linear momentum. Forward momentum from the projectile and escaping gases must be balanced by equal backward momentum of the firearm. After converting inputs to SI units, recoil speed is computed as total forward momentum divided by gun mass.

3) Projectile contribution

Projectile momentum equals m·v. A 10 g projectile at 800 m/s contributes 8.0 N·s. A 4 g projectile at 900 m/s contributes 3.6 N·s. Because momentum scales linearly with velocity, changes in muzzle speed often produce clear recoil differences.

4) Propellant gas contribution

Propellant gases carry momentum too. A common approximation sets gas exit speed to 1.2–1.7 times projectile speed. With 3 g of gas at 1200 m/s, the gas term adds 3.6 N·s. In light firearms, this can be a substantial fraction of total impulse.

5) Unit handling and conversions

You can enter masses in kg, g, lb, or grains, and velocities in m/s or ft/s. The tool converts everything to kg and m/s, then reports recoil velocity in both systems. Momentum is shown as N·s and also as lb·ft/s for reference.

6) Interpreting recoil energy

Recoil energy uses ½ m v². Since energy scales with velocity squared, small speed changes matter. For a 3.2 kg firearm, 3.0 m/s corresponds to about 14.4 J, while 4.0 m/s corresponds to about 25.6 J. Energy is also shown in ft·lbf.

7) Impulse time and average force

If you provide an impulse time, the calculator estimates average force using F̄ ≈ impulse/Δt. Many recoil impulses occur over milliseconds; 3–8 ms is an assumption without pressure curves. Example: 12 N·s over 4 ms gives about 3000 N average force.

8) Practical limitations and checks

This is a free-recoil estimate. It does not model muzzle brakes, suppressors, moving bolts, springs, or shooter coupling. Use it for consistent comparisons. Check realism by increasing gun mass, setting gas mass to zero, and verifying grains and ft/s inputs.

FAQs

1) What is “free recoil”?

Free recoil assumes the firearm moves without external bracing. It estimates the gun’s backward motion from momentum balance before stock padding, stance, or body absorption effects.

2) Should I include propellant gas mass?

Including gas mass improves estimates because gases can contribute meaningful momentum. If you do not know it, start with gas mass set to 0, then test a small value to see sensitivity.

3) What gas velocity factor is reasonable?

A practical engineering range is about 1.2–1.7 times projectile velocity. Use 1.5 as a midrange estimate when you lack measurements or detailed internal ballistics data.

4) Why does the calculator show recoil energy?

Energy helps compare recoil severity because it increases with the square of recoil speed. Two loads with similar impulse can still differ in energy if gun mass or recoil speed changes.

5) How reliable is the average force value?

It is an average over the chosen impulse time, not a peak force. It is most useful for comparisons when you apply the same impulse-time assumption across setups.

6) Does this include muzzle brakes or suppressors?

Not explicitly. Those devices alter gas momentum direction and timing. You can approximate their effect by adjusting the gas term, but the calculator does not simulate device geometry.

7) Why does a heavier gun usually feel softer?

For a given forward momentum, recoil velocity equals momentum divided by gun mass. More mass lowers recoil speed and typically lowers recoil energy, often producing a smoother perceived impulse.