Arrow Kinetic Energy & Momentum Calculator
Kinetic energy (ft·lb and joules) and momentum of an arrow from weight in grains and speed in fps — with the Easton hunting guidelines by game size, downrange energy loss and speed from bow IBO rating.
How it works
KE (ft·lb) = grains × fps² ÷ 450,240; momentum (slug·ft/s) = grains × fps ÷ 225,218; downrange speed ≈ fps × 0.985^(yards ÷ 10); IBO estimate: −2 fps/lb, −10 fps/inch of draw, −1 fps per 3 grains over 350
Kinetic energy is the traditional yardstick for whether an arrow will do its job on game, and the Easton guidelines — 25 to 41 foot-pounds for deer-sized animals, 42 to 65 for elk and boar, more for moose and dangerous game — are quoted everywhere. Because energy rises with the square of speed, fast light arrows look impressive on paper, but experienced hunters weight momentum more heavily: a heavier arrow keeps more of its energy downrange, resists deflection and drives a broadhead through bone better at the same energy. Arrows shed about 1.5% of their speed every ten yards, so the number at the target is what matters. Bow speed ratings are measured under standard conditions, and each pound of draw or inch of draw length below them costs speed.
Worked example
A 420 grain arrow at 285 fps: 75.8 ft·lb of energy and 0.53 slug·ft/s of momentum — enough for the largest game; at 30 yards it still carries about 69 ft·lb.
Frequently asked questions
Is more speed or more weight better for hunting?
For penetration, weight (momentum) wins; for a flat trajectory and margin for range error, speed. Most hunters settle at 6–8 grains per pound of draw weight.
How much energy does a crossbow have?
Typically 100–150 ft·lb with 400 grain bolts at 350–450 fps — far more than a compound, though bolts lose speed faster.
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This calculator is for educational purposes. Double-check important results before acting on them.