Formula
Front-of-center is the AMO measurement. Kinetic energy is Easton’s. The speed estimate only scales the published IBO condition. It is not a model of the cam.
FOC% = 100 × (balance from nock − length / 2) / length
KE = grains × fps² / 450,240
speed ≈ IBO × √((draw weight / 70) × (draw length / 30) × (350 / grains))
450,240 = 7,000 × 32.16 × 2. Momentum in pound-seconds is (grains / 7,000) × fps / 32.174. Joules are foot-pounds times 0.3048 × 4.4482216152605.
Worked examples
30 inch shaft, balance 21 inches from the nock. The midpoint is 15. The balance is 6 inches forward. FOC = 100 × 6 / 30 = 20%.
400 grains at 300 fps. KE = 400 × 300² / 450,240 = 79.96 ft·lbf. At 70 lb, 30 inches, and 350 grains, the estimate equals the IBO number exactly.
Reference
FOC for a 30 inch shaft. Kinetic energy for a 400 grain arrow. Neither column is a minimum. They are the formula at those inputs.
| Balance from nock | FOC | Speed | KE at 400 gr |
|---|---|---|---|
| 16 in | 3.3% | 250 fps | 55.5 ft·lbf |
| 17 in | 6.7% | 270 fps | 64.8 ft·lbf |
| 18 in | 10% | 280 fps | 69.7 ft·lbf |
| 19 in | 13.3% | 300 fps | 80 ft·lbf |
| 20 in | 16.7% | 320 fps | 91 ft·lbf |
| 21 in | 20% | 340 fps | 102.7 ft·lbf |
Questions
How do you calculate arrow FOC?
Balance the arrow on a point and measure from the nock groove to the balance point. FOC percent is 100 times (that distance minus half the arrow length) divided by the arrow length. Length is nock groove to the end of the shaft, not including the point. A 30 inch shaft that balances at 21 inches from the nock is 20% FOC.
How do you calculate arrow kinetic energy?
Grain weight times speed squared, divided by 450,240. That is Easton’s identity. 450,240 is 7,000 grains per pound times 32.16 feet per second squared times 2. A 400 grain arrow at 300 feet per second is 79.96 foot-pounds, about 108 joules.
How does an arrow speed calculator estimate speed?
From the IBO test condition: 70 pounds, 30 inch draw, 350 grain arrow. Speed scales with the square root of (draw weight / 70) × (draw length / 30) × (350 / arrow weight). At that exact setup the estimate equals the IBO rating. A chronograph still wins. Cams, let-off, and the rest move the real number.
Is there a correct FOC?
The AMO definition is a measurement, not a pass/fail. Many bow shops start a hunting arrow somewhere around 10 to 15 percent in front of center and then tune. This page reports the percent. It does not grade it.
Sources
- AMO / ATA front-of-center: 100 × (balance point from the nock groove − length / 2) / length. Length excludes the point.
- Easton kinetic energy: grains × fps² / 450,240.
- IBO / ATA reference condition for a speed rating: 70 lb, 30 in draw, 350 grain arrow.