How to Calculate Kinetic Energy!

To determine your Kinetic Energy (foot pounds) you will need to know the total weight of your arrow in grains and the speed of your arrow in feet-per-second. In order to figure out what those are, you should either purchase a grain scale and chronograph or you can go to your local pro shop where they can determine those measurements for you. If you have all of your own gear, you can determine what your kinetic energy (KE) is by using the following formula:

KE Formula

For an arrow, the kinetic energy is calculated by taking the weight in grains, multiplying it by the velocity squared in feet per second, and dividing by the constant 450,240.

KE = Arrow Weight (mass) x Arrow Speed squared (velocity2) divided (/) by 450,240

The constant is derived from the “1/2” in the formula, converting between grains and pounds (7000 grains per pound weight) and the gravitational constant of 32.16 feet-per-second.

KE formula 2

Here is an example of what a 425 total grain arrow with a measured velocity of 280 fps would produce in terms of foot-pounds of kinetic energy.

KE = [M x V2] / 450,240

KE = [425 x (280)2] / 450,240

KE = [425 x 78,400] / 450,240

KE = 33,320,000 / 450,240

KE = 74.00 foot-pounds

This much Kinetic Energy is enough for that arrow to penetrate and completely pass through a musk ox located 30 yards away.  Of course shot placement matters, so remember: “aim small miss small”.  Happy shooting!

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