FPS to FPE Calculator (Feet per Second to Foot-Pounds)

This calculator converts speed in feet per second (fps) into kinetic energy in foot-pounds (fpe) for a moving object whose weight is given in grains, such as an arrow or a pellet. You also get the energy in joules and the momentum.

Formula

Kinetic energy KE = ½ m v². With weight in grains (7,000 grains = 1 lb) and the standard gravity 32.174049 ft/s² to turn pounds into mass: KE (ft·lbf) = grains × v² ÷ (2 × 32.174049 × 7000) = grains × v² ÷ 450,437. Momentum = grains × v ÷ (7000 × 32.174049). 1 ft·lbf = 1.355818 J.

gr: weight in grains
v: speed in feet per second

Worked Example

A 400-grain arrow at 280 ft/s.

v² = 280 × 280 = 78,400
400 × 78,400 = 31,360,000
31,360,000 ÷ 450,437 = 69.62 ft·lbf
69.62 × 1.355818 = 94.39 J
Momentum = 400 × 280 ÷ 225,218 = 0.4973 slug·ft/s

Limits and common mistakes

Many charts divide by 450,240 instead of 450,437; the difference is under 0.05%.
Energy grows with the square of speed: 10% more speed gives 21% more energy.
Use the measured speed at the distance you care about; it falls with distance.

Formula used

in gr | Projectile weight | grains | 400 | 0 | 100000
in v | Speed | ft/s | 280 | 0 | 10000
out ke | Kinetic energy | ft·lbf | gr / 7000 * v^2 / (2 * 32.174049) | 2
out j | Kinetic energy | J | ke * 1.3558179483314004 | 2
out mom | Momentum | slug·ft/s | gr * v / (7000 * 32.174049) | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Photo collage: archery arrows with fletching in a quiver and a recurve bow on a wooden table. — Save this card: a 1000 × 1500 image of FPS to FPE Calculator (Feet per Second to Foot-Pounds).

Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.

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