Arrow Kinetic Energy Calculator
Calculate arrow kinetic energy from mass and velocity.
See whether your arrow has enough energy for ethical hunting or target shooting performance.
Why kinetic energy matters more than speed
A 350-grain arrow at 320 fps and a 500-grain arrow at 270 fps have nearly identical kinetic energy. But the heavier arrow penetrates better because it carries more momentum, and momentum, not speed, is what drives an arrow through hide, muscle, and ribs. Two arrows can read the same on a chronograph and perform very differently on the animal.
The formula
For an arrow weighed in grains and chronographed in feet per second:
KE (ft-lbs) = (mass in grains × speed²) ÷ 450,240
The constant 450,240 is a unit conversion (7000 grains per pound × twice gravity in ft/s²). The formula is exact, no approximation here.
Ethical hunting energy brackets
These are the working numbers bowhunting authorities and most state game departments publish. They assume a well-tuned setup with a sharp broadhead and a broadside or quartering-away shot.
| Game | Minimum KE (ft-lbs) |
|---|---|
| Small game (rabbit, squirrel) | 25 |
| Whitetail deer, antelope | 40 |
| Mule deer, black bear, caribou | 50 |
| Elk, kudu | 65 |
| Moose, large African plains game | 80 |
| Cape buffalo, brown bear | 100+ |
The trade-off most archers miss
A 30-grain heavier arrow gives up 8 to 10 fps off your chrono number but adds 2 to 4 ft-lbs of KE while improving front-of-center balance and momentum. For hunters at typical 30-yard shots that trade is almost always worth taking. For 3D and target shooters chasing a flatter trajectory, lighter wins.
Worked example
A 400-grain arrow at 280 fps: KE = (400 × 280 × 280) ÷ 450,240 = 31,360,000 ÷ 450,240 = 69.7 ft-lbs
That puts it cleanly into the elk bracket while still flat enough for a 40-yard shot.