Arrow Kinetic Energy Calculator (KE and Momentum)
Arrow kinetic energy in foot-pounds equals arrow weight in grains times velocity in feet per second squared, divided by 450,240. A 420 grain arrow at 280 fps produces 73.1 ft-lbs.
Kinetic energy is the number most archers reach for when they ask whether a setup is enough for an animal. It is worth knowing that it is only half the picture, so this calculator returns momentum alongside it, and flags whether your arrow clears the 5 grain per pound safety floor.
What the formula actually is
Kinetic energy in foot-pounds is weight in grains multiplied by speed in fps squared, divided by 450,240. That constant is not arbitrary: it folds together the 7,000 grains in a pound and the standard gravity conversion, so you can work directly in the units printed on your arrow packaging.
Momentum uses weight times speed divided by 225,218 and is expressed in slug-feet per second. The difference matters more than it sounds. Kinetic energy squares velocity, so it rewards fast, light arrows. Momentum treats weight and speed equally, so it rewards mass. This is the entire heavy-versus-light arrow argument in two equations, and it is why two archers can look at the same setup and disagree about whether it is adequate.
Kinetic energy by game size
These figures are the commonly cited ranges from manufacturers and state agencies, not guarantees. Shot placement, broadhead sharpness and arrow construction all outweigh a few foot-pounds.
| Animal | Commonly cited KE | Notes |
|---|---|---|
| Small game | under 25 ft-lbs | Rabbit, squirrel, most birds |
| Whitetail deer | 25 to 40 ft-lbs | Nearly any modern compound clears this |
| Black bear, hog | 40 to 55 ft-lbs | Heavier bone and hide, favour momentum |
| Elk | 40 to 65 ft-lbs | Arrow build matters as much as the number |
| Moose, large African plains game | 65 ft-lbs and up | Heavy arrows and single-bevel broadheads are the norm |
The one hard rule: 5 grains per pound
Whatever you conclude about energy, do not go under 5 grains of total arrow weight per pound of draw weight. A 60 pound bow needs a 300 grain arrow minimum, a 70 pound bow needs 350. Going under it is effectively a dry fire in slow motion: it dumps energy into the limbs instead of the arrow, and it voids essentially every bow warranty on the market. The calculator above flags this automatically.
Getting an accurate speed number
Kinetic energy is only as good as the velocity you feed it, and the IBO number on your bow is measured under conditions almost nobody shoots: 30 inch draw, 70 pounds, 350 grain arrow. Every inch of draw below 30 costs roughly 10 fps, and every 3 grains of extra arrow weight costs about 1 fps. If you have access to a chronograph at a pro shop, use the real number. Otherwise estimate with our arrow speed calculator, then come back here.
Energy figures only mean something at a known distance, and misjudging 40 yards for 33 is a far more common cause of a bad hit than a few foot-pounds either way. If you shoot past 30 yards or at any angle, a rangefinder with angle compensation does more for your results than chasing arrow speed.
Related tools
- Total arrow weight calculator: build up grain weight from components before you come back here
- Arrow speed calculator: estimate real fps from your bow's IBO rating
- Arrow FOC calculator: front of centre, the other half of penetration
- Arrow spine calculator: make sure the arrow actually flies straight first
Frequently asked questions
How do you calculate the kinetic energy of an arrow?
Kinetic energy in foot-pounds equals total arrow weight in grains multiplied by velocity in feet per second squared, divided by 450,240. So a 420 grain arrow at 280 fps produces 73.1 ft-lbs. The constant 450,240 converts grains and feet per second into foot-pounds, and it already accounts for the 7,000 grains in a pound.
How much kinetic energy do I need for deer?
Most state guidance and manufacturer recommendations put whitetail deer in the 25 to 40 ft-lbs range, and nearly any modern compound setup clears that comfortably. Elk is usually cited around 40 to 65 ft-lbs, and larger animals higher still. Treat these as rough floors rather than targets, because arrow construction, broadhead sharpness and shot placement matter more than the number.
Is kinetic energy or momentum more important for penetration?
Momentum tracks penetration through resistance better than kinetic energy does, which is why heavy-arrow advocates cite it. Kinetic energy scales with the square of speed, so it rewards fast light arrows, while momentum scales linearly with both weight and speed, so it rewards mass. This calculator returns both because they answer different questions, and a setup that looks strong on one can look ordinary on the other.
Does a heavier arrow have more kinetic energy?
Usually yes, but not always, because adding weight also lowers velocity. A heavier arrow retains more energy downrange and is quieter, while a lighter arrow leaves the bow faster and shoots flatter. The practical answer is to run both through the calculator with the speeds your bow actually produces rather than assuming one direction wins.
What is the minimum arrow weight I should shoot?
The near-universal safety floor is 5 grains of total arrow weight per pound of draw weight. A 60 pound bow therefore needs at least a 300 grain arrow. Shooting under that risks damaging the bow and voids most warranties, and it is one of the few genuinely hard rules in arrow building.
How we choose: we compare published manufacturer specifications, verified owner reviews, and pro shop guidance. We do not test gear in person. Draw weight and arrow spine affect safety, so follow your bow manufacturer's specifications and have setup work checked by a qualified pro shop.