⚡ Arrow Kinetic Energy Calculator
Enter your total arrow weight (grains) and arrow speed (feet per second) to calculate kinetic energy at the shot.
The formula behind the foot-pounds
Kinetic energy is ½mv², rewritten so you can feed it grains and feet per second directly. The divisor is 2 × 7000 grains per pound × 32.174 ft/s²:
KE (ft-lbs) = weight (grains) × speed (fps)² ÷ 450436The defaults, a 400 grain arrow at 280 fps, give 400 × 78,400 ÷ 450,436 = 69.6 ft-lbs. Older archery charts divide by 450,240 because they use 32.16 for gravity; at this speed that version returns 69.7, so the two agree to within a rounding step. Output is shown to one decimal place.
Getting the two inputs right
- Weight means the finished arrow. Shaft, insert, point, nock, vanes and wrap, weighed on a grain scale — not the shaft's advertised grains per inch.
- Speed means your speed. Use a chronograph reading from your own bow. An advertised IBO number is measured at a 30 in draw, 70 lb and a 350 grain arrow, so it is rarely what your setup does.
- Speed is squared, weight is not. Ten per cent more speed is 21 per cent more energy; ten per cent more weight is ten per cent more. But adding weight costs speed, so you cannot judge a change on this page alone.
Frequently asked questions
How many foot-pounds do I need to hunt deer?
Published guidance varies and this calculator settles none of it. Your wildlife agency sets the legal minimum, usually written as a minimum draw weight rather than an energy figure, so check the regulations for the place you hunt. Shot placement, arrow flight and a sharp broadhead do more for a clean kill than the last few foot-pounds.
Is a heavier arrow better if it shoots slower?
You cannot tell without a chronograph. Adding grains raises the weight term but lowers the speed term, which is squared, so run both arrows over a chrono and compare the numbers this page returns for each.
What is 350 grains at 300 fps in foot-pounds?
69.9 ft-lbs: 350 × 90,000 is 31,500,000, divided by 450,436. Almost the same answer as the 400 grain, 280 fps default, which is why energy alone rarely picks an arrow.