Arrow Kinetic Energy Calculator

Kinetic Energy vs Momentum in Archery

Kinetic energy measures an arrow's total energy of motion — useful as a rough gauge of how much damage potential it carries on impact. Momentum measures mass in motion differently, weighting arrow mass more heavily relative to speed, and correlates more closely with penetration depth, especially through heavier game or thick hide. Archers often look at both together: a lighter, faster arrow can match a heavier, slower one on kinetic energy while penetrating less deeply, because momentum tells a different part of the story.

How to Use This Calculator

Enter your arrow's total weight in grains (your bow shop or arrow's spine chart can tell you this, or a grain scale gives an exact figure) and its speed in feet per second, measured with a chronograph for accuracy. The calculator returns both kinetic energy and momentum.

How We Calculate It

Kinetic energy (ft-lbs) = (arrow weight in grains × speed in fps²) ÷ 450,240. Momentum (slug-ft/s) = (arrow weight in grains × speed in fps) ÷ 225,400. Both formulas convert grains and feet-per-second into standard physics units before computing the underlying energy and momentum equations.

A Few Notes

The hunting reference ranges above are commonly cited minimums from archery and bowhunting organizations, but actual ethical hunting requirements can vary by state, game type, and local regulations — always check your specific jurisdiction's rules rather than relying solely on a general reference table. Arrow speed also varies with your specific bow setup and can differ meaningfully from a manufacturer's advertised speed, so a chronograph reading from your actual setup gives a far more accurate number than an estimate.