Hong Life CalculatorsUnderstanding the recoil energy calculator — concept and principle
Recoil is the backward push of a firearm when it fires. This calculator estimates free recoil energy and velocity with the method published by SAAMI, using the firearm's weight, the projectile weight, the powder charge and the muzzle velocity, with a powder-gas factor for rifles, shotguns and handguns.
How it is calculated
Recoil velocity V = (WE × VE + WPC × f × VE) ÷ (7,000 × WF)
Free recoil energy = WF ÷ 64.34 × V² (ft·lbf)
Recoil momentum = WF ÷ 32.17 × V (lbf·s)
- WE projectile (or shot plus wad) weight and WPC powder charge, in grains; VE muzzle velocity in fps; WF firearm weight in lb including scope.
- f is the powder-gas velocity factor: 1.75 for high-powered rifles, 1.50 for average shotguns and handguns, 1.25 for long-barrel shotguns.
- 7,000 grains = 1 lb; 64.34 = 2 × 32.17 ft/s².
The principle
Momentum is conserved. When the bullet and the powder gases are pushed forward, the firearm is pushed backward with equal momentum. The gas leaves the muzzle faster than the bullet, which is why its contribution uses a higher velocity, f × VE. Dividing the total forward momentum by the gun's mass gives its backward velocity, and kinetic energy ½mv² gives the recoil energy. A heavier gun moves back more slowly, and since energy depends on velocity squared, its recoil energy falls sharply.
Worked example
Default inputs: high-powered rifle (f = 1.75), 8-lb rifle, 150-grain bullet, 46 grains of powder, 2,820 fps.
- Bullet momentum term = 150 × 2,820 = 423,000.
- Gas term = 46 × 1.75 × 2,820 = 227,010 (gas velocity 4,935 fps).
- V = 650,010 ÷ (7,000 × 8) = 11.61 fps = 3.54 m/s.
- Free recoil energy = 8 ÷ 64.34 × 11.61² = 16.8 ft·lbf = 22.7 J.
- Recoil momentum = 8 ÷ 32.17 × 11.61 = 2.89 lbf·s; firearm weight = 3.63 kg.
| Muzzle velocity (fps) | Free recoil energy (ft·lbf) |
|---|---|
| 705 | 1 |
| 1,410 | 4.2 |
| 2,115 | 9.4 |
| 2,820 | 16.8 |
| 3,525 | 26.2 |
| 4,230 | 37.7 |
| 5,640 | 67 |
How to read the result
Free recoil energy is a standard way to compare loads and firearms. Heavier guns, lighter bullets and lower velocities reduce it. Felt recoil also depends on stock fit, recoil pads, muzzle brakes and the shooter's position, which this calculation does not include. SAAMI's own example of a typical 12-gauge load comes out around 30 ft·lb.
Common mistakes
- Using the bare rifle weight without the scope and mount.
- Leaving out the powder charge, which noticeably underestimates recoil.
- Using the wrong gas factor for the firearm type.
- Comparing free recoil with felt recoil as if they were the same.
Frequently asked questions
What is free recoil?
The recoil energy if the gun could move backward freely, without the shooter holding it.
Why does the powder charge matter?
The powder gas is ejected at high speed and adds significantly to the momentum.
How can I reduce recoil?
A heavier gun, a lighter load, a recoil pad or a muzzle brake can help.
What does SAAMI stand for?
Sporting Arms and Ammunition Manufacturers' Institute, a US standards organisation.
Sources: SAAMI, "Gun Recoil – Technical: Free Recoil Energy" (rev. 7/9/2018)