Enter the weight (grains) and the velocity (fps) into the calculator to determine the FPE. This calculator can also determine the weight or velocity if the other variables are known.
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FPE Formula
FPE = (weight_grains * velocity_fps^2) / 450240
- FPE — kinetic energy in foot-pounds (ft-lbs)
- weight_grains — projectile mass in grains (7000 grains = 1 lb)
- velocity_fps — projectile velocity in feet per second
- 450240 — conversion constant (2 × 7000 × 32.174)
The other modes use:
Momentum (slug·ft/s) = (weight_grains / 7000 / 32.174) * velocity_fps
Velocity_fps = sqrt((FPE * 450240) / weight_grains)
FPE is muzzle energy at the velocity you enter. It does not account for drag, so downrange energy will be lower. Joules conversion uses 1 ft-lb = 1.35582 J.
Reference Values
Typical muzzle energies for common projectiles:
| Cartridge / Pellet | Weight | Velocity | FPE |
|---|---|---|---|
| .177 airgun (UK legal) | 8 gr | 820 fps | ~12 ft-lbs |
| .22 airgun (PCP) | 14.3 gr | 900 fps | ~26 ft-lbs |
| .22 LR | 40 gr | 1080 fps | ~104 ft-lbs |
| 9mm Luger | 124 gr | 1150 fps | ~364 ft-lbs |
| .223 Rem | 55 gr | 3240 fps | ~1282 ft-lbs |
| .308 Win | 150 gr | 2800 fps | ~2611 ft-lbs |
| Hunting arrow | 500 gr | 280 fps | ~87 ft-lbs |
Common energy thresholds used for legal and quarry guidance:
| FPE | Reference |
|---|---|
| ≤ 7.5 ft-lbs (10 J) | Germany / many EU airgun limit |
| ≤ 12 ft-lbs | UK air rifle limit (no FAC) |
| ≤ 6 ft-lbs | UK air pistol limit |
| ~25 ft-lbs | Common minimum for rabbit-class quarry |
| ~65 ft-lbs (arrow) | Recommended minimum for whitetail deer |
| ~1000 ft-lbs | Rule-of-thumb minimum for deer (firearm) |
Worked Example
A 124 gr 9mm bullet leaves the muzzle at 1150 fps:
FPE = (124 × 1150²) / 450240 = (124 × 1,322,500) / 450240 = 364.2 ft-lbs
Why divide by 450240? Standard kinetic energy is ½mv². To go from grains and feet-per-second to foot-pounds, you convert grains to slugs (divide by 7000 grains/lb and 32.174 ft/s²) and apply the ½ factor. The combined constant is 2 × 7000 × 32.174 ≈ 450240.
FPE vs. momentum: Energy scales with the square of velocity, so light fast projectiles look impressive on paper. Momentum scales linearly with velocity, so heavy slow projectiles (arrows, big bore) rate higher there. For penetration on game, both numbers matter.
Does FPE equal stopping power? No. Energy is one input. Bullet construction, shot placement, and penetration depth determine terminal effect. Use FPE as a comparison metric, not a guarantee.
