Formula and Method for Foot-Pounds of Energy (FPE)
Foot-pounds of energy (FPE) is the standard measure of kinetic energy used by bowhunters, shooters, and ballisticians to describe how much energy a bullet or arrow delivers on impact. It comes from the same physics as any kinetic energy calculation, KE = ½mv², but is expressed in the customary units the shooting sports use: projectile weight in grains and velocity in feet per second (fps).
How the calculation works
Enter the projectile's weight and velocity in whichever units you have, and the calculator converts weight to grains and velocity to feet per second. Weight (a force, in pounds) must first be converted to mass in slugs by dividing by standard gravity (32.16 ft/s²), and grains are converted to pounds by dividing by 7,000 (there are 7,000 grains in a pound). Combining those conversions with KE = ½mv² collapses to the well-known ballistics shortcut: KE (ft-lbs) = (Weight in grains × Velocity² in fps) ÷ 450,240. The calculator also reports the same energy in joules (1 ft-lb ≈ 1.35582 J) and the projectile's momentum (p = mv) in slug·ft/s and kg·m/s, since energy and momentum describe different things about an impact.
Common mistakes
- Mixing up weight units: grains are the standard weight unit in archery and ballistics; entering a bullet or arrow's weight in ounces or pounds without converting will give a wildly wrong FPE.
- Using an average velocity instead of impact velocity: FPE calculated from chronograph (muzzle) velocity is the maximum energy; actual energy on target is usually lower because the projectile slows down over distance due to drag.
- Treating FPE as the whole story: two projectiles with the same FPE can behave very differently on impact — a heavy, slow arrow and a light, fast arrow can have equal kinetic energy but very different momentum and penetration.
Real-world applications
- Bowhunters compare arrow FPE against organizations' minimum-energy guidelines to judge whether a setup is adequate for a given game animal.
- Firearm and ammunition manufacturers publish muzzle energy in ft-lbs so shooters can compare cartridges and loads on equal footing.
- Airgun and pellet gun shooters use FPE to classify power levels for hunting, target shooting, and legal power-limit compliance.
- Ballisticians consider momentum alongside FPE because momentum, not energy alone, strongly influences penetration depth in terminal-ballistics models.