Arrow Kinetic Energy Calculator
Calculate arrow kinetic energy and momentum to determine hunting adequacy for different game sizes.
About this calculator
This calculator converts your arrow's weight and speed into kinetic energy and momentum, the two figures archers use to judge whether a hunting setup is adequate for a given game size. Kinetic energy (KE) is computed with the standard archery formula KE = weight(grains) x speed(fps)^2 / 450,240, which is simply the physics equation KE = 1/2 m v^2 with mass converted from grains to slugs. Because velocity is squared, Arrow Speed is the input this calculator's Kinetic Energy result is most sensitive to: a given percentage increase in speed moves KE roughly twice as much as the same percentage increase in Arrow Weight, since a squared term compounds faster than a linear one.
Momentum, in contrast, scales identically with both weight and speed (mass times velocity, with neither term squared), and many bowhunters consider it a better predictor of penetration than kinetic energy alone, since a heavier, slower arrow can retain more momentum through impact than a lighter, faster arrow with the same KE. The Hunting Classification output maps your computed KE against commonly cited archery guidelines (roughly 25+ ft-lbs for small game, 42+ for medium game like deer, 65+ for large or dangerous game) -- these are widely used industry rules of thumb, not a specific state's legal minimum, and actual hunting regulations on minimum bow, arrow, or energy requirements vary by state and by game species, so always confirm your own jurisdiction's rules before hunting. This calculator does not account for broadhead type, shot placement, or arrow FOC (front-of-center balance), all of which also meaningfully affect real-world penetration.
Inputs
Results
Kinetic Energy
69.65 ft-lbs
Hunting Classification
Dangerous Game (moose, grizzly)
How to Use This Calculator
- Enter your Total Arrow Weight in grains (use the Arrow Build calculator to find this).
- Set your Arrow Speed in fps using a chronograph at the shooting line.
- Review Kinetic Energy in ft-lbs — 25+ for deer, 42+ for elk, 65+ for large dangerous game.
- Check Momentum for penetration assessment — higher momentum drives deeper.
- Use the Hunting Classification to confirm your setup meets the energy minimum for your target game.
How the result changes with Arrow Speed
| Arrow Speed | Kinetic Energy | Hunting Classification |
|---|---|---|
| 140 | 17.41 ft-lbs | Small Game (rabbit, turkey) |
| 210 | 39.18 ft-lbs | Medium Game (deer, antelope) |
| 400 | 142.15 ft-lbs | Dangerous Game (moose, grizzly) |
What each input means
- Arrow Weight
- Total arrow weight in grains (shaft + point + vanes + nock).
- Arrow Speed
- Chronographed arrow speed in feet per second.
What each result means
- Kinetic Energy
- Arrow energy — 25+ for deer, 42+ for elk, 65+ for large dangerous game.
- Momentum
- Arrow momentum — higher momentum means better penetration.
- Hunting Classification
- Maximum game class based on kinetic energy.
How this is calculated
Worked example, using the default values
- Identify Input ParametersArrow Weight = 400, Arrow Speed = 280 = 2 input(s) provided
- Calculate Kinetic EnergyKinetic Energy69.65 = 69.65
- Calculate MomentumMomentum0.4973 = 0.4973
Engine last updated . Checked against 2 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does Arrow Speed affect Kinetic Energy more than Arrow Weight does?
Kinetic energy is proportional to the square of velocity but only linearly proportional to mass, so a given percentage increase in Arrow Speed roughly doubles its effect on Kinetic Energy compared to the same percentage increase in Arrow Weight. That's a direct consequence of the KE = 1/2 m v^2 formula this calculator uses, not an archery-specific design choice.
Is Momentum or Kinetic Energy more important for hunting?
Many bowhunters consider Momentum the better predictor of penetration, because it scales identically with weight and speed rather than favoring speed the way Kinetic Energy does. A heavier, slower arrow can carry more momentum through an animal than a lighter, faster arrow with an identical Kinetic Energy figure, which is why some hunting setups are built around momentum rather than raw KE alone.
Are the Hunting Classification thresholds a legal requirement?
No -- the kinetic-energy thresholds used here (roughly 25, 42, and 65 ft-lbs) are widely cited industry rules of thumb from archery equipment manufacturers and bowhunting organizations, not a specific state's law. Actual minimum draw weight, arrow weight, or kinetic energy requirements for bowhunting vary by state and by game species, so check your own state wildlife agency's regulations before hunting.
Why do heavier arrows sometimes have lower Kinetic Energy than lighter ones?
Kinetic Energy depends much more heavily on speed than on weight because speed is squared in the formula. A heavier arrow shot from the same bow typically leaves the string slower, and if that speed loss is proportionally larger than the weight gain, the heavier arrow's Kinetic Energy can end up lower even though it weighs more.
What doesn't this calculator account for?
It only computes Kinetic Energy and Momentum from weight and speed -- it doesn't factor in broadhead type or sharpness, shot placement and angle, arrow FOC (front-of-center balance), or the animal's actual anatomy, all of which meaningfully affect real-world penetration and lethality independent of the raw energy numbers.
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