Free · Physics models
Ideal Momentum Recoil Estimate
Estimate free recoil speed, energy and impulse from projectile and propellant-gas momentum.
- Formula & worked example
- Private in your browser
- No signup
Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
Private by default
Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.
Formula and method
A 10 g projectile at 100 m/s and 1 g gas mass at 1,000 m/s give total momentum 2 kg·m/s; a 2 kg free body recoils at 1 m/s with 1 J energy.
M v = mb vb + mg vg; E = M v²/2.
Worked example
Enter these known values and leave the other values blank.
- Mass of bullet (Mb)
- 10 g
- Velocity of bullet (Vb)
- 100 m/s
- Mass of powder charge (Mc)
- 1 g
- Velocity of charge (Vc)
- 1000 m/s
- Mass of firearm (Mf)
- 2 kg
- Velocity of firearm (Vf)
- 1 m/s
- Recoil energy (Er)
- 1 J
- Recoil impulse (I)
- 2 N⋅s
Assumptions and limitations
- Ideal linear momentum balance for free recoil. The gas velocity is an effective modeling input.
- The retained example presets are approximate; the model omits external support, recoil mechanisms, muzzle devices and detailed gas dynamics.
- This is a mechanics comparison and does not specify ammunition construction or operating limits.
- Enter known quantities and clear the unknown to use available inverse branches. Locks retain supplied values. Consistency messages cover fully visible equations; identities with hidden dependencies may require a manual consistency check. Preset values are illustrative approximations, and unit selectors preserve the underlying quantity.
Common questions
How do I solve for a different quantity?
Clear that quantity and supply enough independent known values. Some outputs are one-way or tied to a selected preset, so they cannot determine every input.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.