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Kinetic Energy Calculator

This calculator works out an arrow’s kinetic energy (KE) — a rough measure of the energy the arrow carries, in foot-pounds (ft-lbs). Enter the arrow’s total weight in grains and its speed in feet per second (fps), and it returns KE using the standard archery formula: KE (ft-lbs) = (arrow weight in grains × speed in fps²) ÷ 450,240.

Calculate your arrow’s kinetic energy

The total finished weight of the arrow (shaft, point, insert, nock, and fletching). Weigh it on a grain scale.

Measured speed in feet per second, ideally from a chronograph with your exact arrow. The bow’s rated speed (e.g. an ATA/IBO figure) is measured with a specific test arrow, so it gives a higher, rougher estimate than your own setup.

Enter your arrow weight and speed above to see your kinetic energy. With JavaScript turned off, use the formula below to work it out by hand.

The formula, shown

Arrow kinetic energy is a simple, standard calculation — there’s nothing proprietary about it, so here it is in full:

  1. Weigh the finished arrow (m), in grains.
  2. Measure the arrow’s speed (v), in feet per second — ideally with a chronograph and your exact arrow.
  3. Square the speed: v × v.
  4. Multiply the weight by the squared speed: m × v².
  5. Divide by the constant 450,240: KE (ft-lbs) = (m × v²) ÷ 450,240.

The 450,240 constant converts grains and feet-per-second into foot-pounds in one step (it folds in the conversion from grains to pounds of mass and the ½mv² of the physics definition), which is why the formula looks so tidy.

Worked example: a 400-grain arrow travelling at 280 fps has v² = 78,400, so m × v² = 400 × 78,400 = 31,360,000. Divide by 450,240 and KE = 69.7 ft-lbs (rounded to one decimal). You can check that result in the calculator above.

What kinetic energy is and what it’s used for

Kinetic energy is the energy an object carries because it is moving. For an arrow it depends on just two things: how heavy the arrow is and how fast it is going — and because speed is squared in the formula, speed has a larger effect than weight for a given change. KE is reported in foot-pounds (ft-lbs) and is one common way to put a single number on “how much an arrow is carrying” downrange.

Archers use KE as a rough comparison figure — for instance, to see how a heavier point or a faster setup changes the energy an arrow delivers, or to compare two arrow builds on the same bow. It is a useful shorthand, but it is only one part of the picture: penetration and terminal performance also depend on arrow weight distribution, momentum, point and broadhead design, and how cleanly the arrow flies. KE alone does not tell the whole story.

Kinetic energy starts with how much energy your bow can store, which is driven largely by draw weight. For related definitions, see the archery terms glossary.