Arrow Kinetic Energy Calculator

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Calculator

Use this arrow kinetic energy calculator to get kinetic energy in foot-pounds and momentum from your arrow weight and speed. If you have not chronographed the bow, it estimates arrow speed from the IBO rating, your draw weight, draw length and arrow weight, or from a crossbow's rated speed and bolt weight.

Arrow Weight Calculator Minimum Draw Weight for Bow Hunting Crossbow Bolt Weight Chart Archery Tools

Live calculator

Kinetic energy grows with the square of speed, so speed matters more than weight for energy. Momentum grows in a straight line with both.

Calculate kinetic energy and momentum

Formulas: KE (ft-lb) = arrow weight (gr) × speed (fps)² ÷ 450,240. Momentum (slug·ft/s) = weight × speed ÷ 225,218.

A chronograph reading beats any estimate. The IBO method is usually within about 10 fps.
Energy at the target is lower than at the bow. Expect roughly 1.5 to 2 fps lost per yard.
Kinetic energy is not the whole story for hunting: momentum, broadhead design and shot placement matter as much.

Kinetic energy guidelines for hunting

The most quoted guideline comes from Easton and is used in most hunter-education material. It is a guide for ethical setups at normal bowhunting distances, not a legal rule. Many states set a minimum draw weight instead, covered in minimum draw weight for bow hunting.

Kinetic energy at the bow	Game class	Typical setup that gets there
Under 25 ft-lb	Small game: rabbits, squirrels	Youth bows, light recurves
25 to 41 ft-lb	Medium game: whitetail, mule deer, antelope	40 to 50 lb compound, 45 to 55 lb recurve
42 to 65 ft-lb	Large game: elk, black bear, wild boar	55 to 70 lb compound with a 400+ grain arrow
65 ft-lb and above	Toughest game: moose, grizzly, cape buffalo	70 lb+ compound with a heavy arrow, most hunting crossbows

Remember that energy drops with distance. A setup that makes 45 ft-lb at the bow may deliver 38 ft-lb at 40 yards.

Typical arrow speed, energy and momentum

Setup	Arrow weight	Speed	Kinetic energy	Momentum
25 lb youth recurve	300 gr	150 fps	15 ft-lb	0.200
40 lb recurve	400 gr	180 fps	29 ft-lb	0.320
50 lb compound	400 gr	255 fps	58 ft-lb	0.453
60 lb compound	420 gr	280 fps	73 ft-lb	0.522
70 lb compound	450 gr	295 fps	87 ft-lb	0.589
400 fps crossbow	400 gr	400 fps	142 ft-lb	0.710

Momentum in slug·ft/s. All numbers are at the bow with typical arrows; your bow will differ.

How the speed estimate works

IBO speed is measured at 70 lb, 30 inches of draw and a 350-grain arrow with nothing on the string. The estimate applies the rules of thumb bow makers and pro shops use:

Draw lengthAbout 10 fps for every inch shorter or longer than 30 inches.

Draw weightAbout 2 fps for every pound below or above 70 lb.

Arrow weightAbout 1 fps for every 3 grains heavier or lighter than 350 grains.

String accessoriesAbout 1 fps for every 3 grains of peep, loop and silencers on the string.

For crossbows the calculator uses about 3 fps per 10 grains of bolt weight away from the rating weight, which matches published maker tables closely.

Kinetic energy vs momentum

Kinetic energy rewards speed because speed is squared in the formula. Momentum rewards weight and speed equally, and it is a better predictor of how far an arrow keeps pushing through hide, muscle and bone once it hits. That is why two setups with the same kinetic energy can behave differently: a heavy, slower arrow carries more momentum and usually penetrates better with a fixed-blade broadhead. Most bowhunting guidance treats 0.40 slug·ft/s or more as comfortable for deer and 0.55 or more for elk-sized game. Use the arrow weight calculator to see how adding point weight changes total grains and grains per pound, and the FOC calculator to keep the balance forward when you add weight up front.

Related tools and guides

Energy is one output of the whole setup. These pages cover the inputs.

Arrow Weight Calculator Arrow Spine Calculator Arrow FOC Calculator Minimum Draw Weight for Bow Hunting Crossbow Bolt Weight Chart How Far Will a Crossbow Shoot?Can a Bow and Arrow Kill You?Bow Draw Weight Chart

Frequently asked questions

Short answers to the questions people ask most about this tool.

How do you calculate arrow kinetic energy?

Multiply the arrow weight in grains by the speed in feet per second squared, then divide by 450,240. A 420-grain arrow at 280 fps makes 73 ft-lb.

How much kinetic energy do you need to kill a deer?

The common guideline is 25 to 41 ft-lb at the bow for deer-sized game, with good shot placement and a sharp broadhead. Most 40 lb+ compounds and 45 lb+ recurves reach it.

How much kinetic energy for elk?

Guidelines put elk in the 42 to 65 ft-lb class. A 60 to 70 lb compound with a 420 to 500 grain arrow gets there with margin for distance.

Is momentum or kinetic energy more important for bowhunting?

Both matter. Kinetic energy is the number most guidelines quote, but momentum tracks penetration better. A heavier arrow trades a little energy for more momentum and quieter shooting.

How accurate is an IBO speed estimate?

Usually within 10 fps when the bow is tuned and the inputs are honest. A chronograph is always better, and cheap ones are accurate enough for this.

Does arrow speed drop with distance?

Yes. Expect roughly 1.5 to 2 fps of loss per yard from drag, so a 280 fps arrow arrives at 30 yards around 230 to 235 fps.

Can I use this for crossbow bolts?

Yes. Choose the crossbow option, enter the rated speed, the bolt weight the rating used, and your actual bolt weight.

References

These sources support the formulas and guidance on this page.