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Recoil Energy Calculator

Calculate the recoil of firearms using the recoil energy calculator.

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Free recoil energy25.7574 J19 foot-pounds — this is what is felt, and it is a small fraction of the muzzle energy
Muzzle energy3.5398 kJ2,610.8 foot-pounds
Muzzle velocity853.44 m/s2,800 fps, Mach 2.488 at sea level
Projectile mass9.7198 g150 grains
Momentum8.2953 kg·m/swhat determines recoil, unlike energy
Taylor knock-out factor18.48an old empirical index, not a physical quantity — included because it is widely quoted
Sectional density0.2259mass in pounds ÷ diameter in inches squared — how much mass sits behind each unit of frontal area
Ballistic coefficient0.2378sectional density ÷ form factor 0.95 — higher resists drag better and retains velocity further
Relative drag deceleration4.2056the inverse: this is what actually slows the bullet
Frontal area48.068 mm²
Energy per unit frontal area7.364e+7 J/m²the figure that governs penetration far better than energy alone
Free recoil velocity3.7828 m/sfrom conservation of momentum, including the powder gas at a conventional 1.75× muzzle velocity
Recoil as a share of muzzle energy0.728%momentum is shared equally; energy is not, and the heavier body gets far less of it
Recoil energy at twice the firearm mass12.8787 Jhalved — which is why a heavy rifle kicks less

The formula

KE = ½mv²; sectional density = m ÷ d²; BC = SD ÷ form factor

Momentum is shared, energy is not

Firing a projectile conserves momentum: the gun and the bullet take equal and opposite momentum. Energy is a different matter. Kinetic energy is p²/2m, so for the same momentum the heavier body gets far less energy — which is why a 3.6 kg rifle receives only a small percentage of the muzzle energy as recoil, and why a heavier gun kicks less for the same cartridge.

The powder gas carries momentum too, and it leaves the muzzle faster than the bullet. Ignoring it understates recoil noticeably in high-capacity cartridges. The convention used here is to count the charge at 1.75 times the muzzle velocity, which is a fitted rule rather than a derivation.

Ballistic coefficient is sectional density divided by a form factor — how much mass sits behind each unit of frontal area, adjusted for how streamlined the shape is. A high figure means the projectile sheds velocity slowly, which matters far more at long range than muzzle energy does. Note that a BC is quoted against a specific reference projectile (G1, G7 and others), and the same bullet has different numbers under each, so figures are only comparable within one standard.