How this calculator works
Conservation of momentum gives equal and opposite firearm and ejecta momentum in an initially stationary, freely moving system. The gas term can be significant, so enter a supported effective gas velocity rather than treating it as a universal constant. This model excludes the shooter, recoil mechanisms, muzzle brakes and time-dependent force. No firearm or ammunition presets are assumed.
Formula
I = m_b v_b + m_g v_g; v_r = I/M; E_r = I^2/(2M).
Worked example
With 0.01 kg at 400 m/s and 0.001 kg of gas at 1000 m/s, impulse is 5 N s. A 4 kg firearm has recoil speed 1.25 m/s and free recoil energy 3.125 J.
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Frequently asked questions
Is this felt recoil?
No. Felt recoil also depends on support, recoil duration, firearm geometry and moving mechanisms.
Why enter gas speed separately?
Gas momentum is part of the momentum balance and varies with the system.
Can I compare two firearm masses?
At fixed ejecta impulse, doubling firearm mass halves free recoil energy and recoil speed.