Arrow kinetic energy calculator

Use the complete arrow weight and its own speed

Enter arrow weight in grains and speed in feet per second, or fps. Include the point, shaft, insert, nock, fletching, and any other installed parts in the weight. A grain is a unit of mass used for arrows; it is different from a gram. The arrow grain guide explains the notation you will see on component labels.

Match the speed to the arrow you weighed. Combining a heavy hunting arrow's mass with the advertised speed of a bow tested using a lighter arrow overstates the result. If the arrow has not been assembled, use the arrow weight calculator and keep the result marked as a planning estimate.

A chronograph reading describes speed at its measurement location. Energy calculated from a reading near the bow describes the arrow there. Air resistance reduces speed in flight, so this number cannot be treated as impact energy at an arbitrary target distance.

The kinetic energy and momentum formulas

Kinetic energy is the energy an arrow has because it is moving. In the units used here, KE (ft-lb) = arrow weight in grains x speed in fps squared / 450,240. Square the speed before multiplying by arrow weight. The denominator converts grains and feet per second into foot-pounds.

Momentum describes the arrow's mass multiplied by its velocity. For forward arrow flight, momentum (slug-ft/s) = arrow weight in grains x speed in fps / 225,120. The slug is a unit of mass in this measurement system. Momentum and energy use different units, so their numerical values should not be compared directly.

Keep the full input values during calculation and round the final answer. Two decimal places for energy and three for momentum are enough for most setup comparisons. Extra decimal places do not compensate for a guessed speed or an arrow weight copied from a component catalog.

Why weight and speed change the results differently

With arrow weight fixed, a 10 percent increase in speed raises momentum by 10 percent and kinetic energy by 21 percent. That difference comes from squaring speed in the energy formula. With speed fixed, adding 10 percent to arrow mass raises both calculated quantities by 10 percent.

In a real bow, mass and speed are linked. A heavier arrow generally leaves the same bow more slowly and often carries more momentum. You need both new measurements to know how much the result changes. Holding speed constant while adding arrow weight is useful for explaining the formula, but it is not a prediction for a bow.

For example, the 400 grain arrow at 280 fps has about 69.65 ft-lb of energy and 0.498 slug-ft/s of momentum. An illustrative 500 grain arrow at 250 fps has about 69.41 ft-lb and 0.555 slug-ft/s. Those arrows have nearly equal energy, while the heavier example has greater momentum. The speeds in this example are hypothetical; measure both arrows on your own bow for a usable comparison.

Example energy and momentum ranges

The examples below span about 22 to 100 ft-lb of energy. They show what different weight and speed inputs produce, without assigning a performance rating to a bow. Use them to check the scale of your result rather than as hunting thresholds or recommended builds.

Choose an arrow that meets the bow manufacturer's minimum weight and suits the bow's specifications before comparing these outputs. An attractive energy figure does not establish that a shaft is correctly spined or safe to shoot. If you need a provisional speed input, the arrow speed calculator explains the assumptions behind an IBO estimate.

What these numbers can tell a hunter

Kinetic energy and momentum are useful descriptions of a setup, but neither calculation predicts penetration by itself. Arrow flight, broadhead design and sharpness, impact angle, and the material struck affect the result. A calculator cannot turn those variables into a reliable penetration distance or guarantee a clean outcome.

Before choosing between a lighter, faster arrow and a heavier, slower one, weigh each complete build and measure its speed. Then assess arrow flight and your ability to place the shot. There is little value in ranking builds by a small numerical difference while one flies poorly.

Front-of-center balance is a separate measurement. The FOC calculator describes how mass is distributed along the arrow; energy and momentum use total mass. Two arrows with the same weight and speed can have the same calculated outputs and different balance points.

Keep comparisons tied to a test setup

Write down the finished arrow mass, speed readings, and bow settings for each build. When a point change alters mass, measure speed again rather than carrying the old speed into a new calculation. Keep launch measurements separate from any downrange measurements, and compare results taken at the same location.

These formulas do not establish legal hunting minimums or recommend a setup for a species. Check the rules that apply where you hunt and get equipment advice for your actual bow and intended use. Keep that decision separate from the arithmetic in this calculator.

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