Kinetic Energy Calculator
Kinetic energy is the arrow's total work capacity, in foot-pounds. Enter your arrow's true weight and its real speed — measured or estimated — and see the energy, with the momentum alongside.
How Arrow KE Is Calculated
Kinetic energy is half the mass times the square of the velocity. In archery units — grains and feet per second — that works out to one division:
The constant 450,240 folds together the grains-in-a-pound conversion (7,000) and gravitational acceleration, so the answer lands directly in foot-pounds. Two consequences follow from the squared speed: doubling speed quadruples energy, while doubling arrow weight only doubles it — and adding weight always costs speed, which is the trade every arrow build negotiates. The momentum calculator scores that same trade the other way, which is why serious setups check both.
Your inputs matter more than the arithmetic. If the speed came from a maker's IBO rating rather than a chronograph or the arrow speed calculator's estimate, the energy figure inherits the rating's optimism.
Kinetic Energy Guidance by Game
These are the ranges reproduced across manufacturer and bowhunting guidance for decades. They are rules of thumb for a well-placed shot with a sharp broadhead — not guarantees, and not a substitute for your local regulations.
| Kinetic energy | Commonly cited for |
|---|---|
| Under 25 ft-lb | Small game — rabbit, squirrel, turkey with suitable heads |
| 25–41 ft-lb | Deer-sized game — the classic whitetail band |
| 42–64 ft-lb | Large game — elk, moose, black bear, caribou |
| 65 ft-lb + | The largest and toughest game, heavy arrows assumed |
Read the table with the FOC calculator in mind: two arrows with identical KE penetrate differently if one is built with its weight forward and a quality broadhead. Energy is the entry ticket; arrow build decides how much of it arrives.
KE Worked Examples
The homepage setup — 450 grains at 286 fps: 450 × 286² ÷ 450,240 = 81.8 ft-lb, roughly double the top of the deer band.
A 400-grain target-weight arrow at 300 fps: 400 × 300² ÷ 450,240 = 80.0 ft-lb — nearly the same energy from a very different build.
A 600-grain traditional arrow at 245 fps: 600 × 245² ÷ 450,240 = 80.0 ft-lb. Same energy again — but its momentum (see the momentum page) is about 23% higher.
Limits of the KE Number
Kinetic energy is measured at the bow. Drag starts spending it immediately, broadheads spend it faster than field points, and none of the figure accounts for arrow flight quality — a poorly tuned arrow wobbling into the target wastes energy no formula can refund. Treat KE as a comparison between your own setups, not an absolute verdict on any one of them.
Kinetic Energy FAQs
How much kinetic energy do I need for deer?
The figure most often cited is 25–41 ft-lb for deer-sized game, with the strong majority of modern compound setups producing far more — a 450-grain arrow at 280 fps makes about 78 ft-lb. Shot placement and a sharp broadhead matter more than chasing a bigger number once you are past the commonly cited range.
How is arrow kinetic energy calculated?
Kinetic energy in ft-lb is arrow weight in grains multiplied by speed in fps squared, divided by 450,240 — a constant that folds in the grains-to-pounds conversion and gravity. This calculator does exactly that sum, and shows the working under the result.
Does a faster arrow always have more kinetic energy?
Not necessarily. Energy grows with the square of speed but only in direct proportion to weight, so a light, fast arrow and a heavy, slow one can carry identical energy. A 400-grain arrow at 300 fps and a 600-grain arrow at 245 fps both make about 80 ft-lb — the momentum calculator shows where they differ.
How much kinetic energy does my arrow lose at 40 yards?
An arrow sheds speed to air resistance from the moment it leaves the bow. On the drag model this site uses, a 286 fps arrow is doing about 273 fps at 40 yards and has lost roughly 9% of its muzzle energy. The arrow speed calculator shows speed and KE at 10-yard steps out to 50.
Is more kinetic energy always better for hunting?
Up to a point. Past the commonly cited range for your game, extra energy buys little, and it usually arrives attached to a slower, louder or harder-to-tune setup. Experienced bowhunters tend to optimise momentum and arrow build next, which is why this site pairs every KE figure with its momentum.
- Easton Archery — shaft selection charts — the reference spine-selection and arrow-building charts this site’s groupings follow
- Ashby Bowhunting Foundation — Dr Ed Ashby’s arrow penetration research — the source of the momentum and FOC guidance
- IBO (International Bowhunting Organization) — the body behind the IBO speed-rating standard: 70 lb, 30 in draw, 350-grain arrow