Calculate projectile foot-pounds of energy from weight and velocity, compare two loads, or solve for required velocity or weight in ft-lb.
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Foot-Pounds of Energy Formula
The calculator uses the standard kinetic energy equation, rewritten so you can plug in projectile weight in grains and velocity in feet per second directly.
KE = (m * v^2) / 450,436
- KE = kinetic energy in foot-pounds (ft-lb)
- m = projectile weight in grains (gr)
- v = projectile velocity in feet per second (ft/s)
- 450,436 = unit conversion constant (2 × 7000 gr/lb × 32.174 ft/s² gravitational conversion)
The constant 450,436 lets you skip converting grains to slugs and feet per second to the SI base. Energy scales linearly with weight but with the square of velocity, so doubling velocity quadruples energy. The figure is a muzzle or point-of-measurement value only. It does not account for drag, drop, or terminal performance.
For metric inputs the calculator first converts to grains and ft/s, runs the same formula, then converts the output to joules using 1 ft-lb = 1.3558 J.
The three modes use the same formula in different ways:
- Energy mode: solves KE directly from weight and velocity.
- Compare mode: runs the formula on two loads and reports the difference in ft-lb and percent.
- Reverse mode: rearranges the formula. To find velocity, v = sqrt(KE × 450,436 / m). To find weight, m = (KE × 450,436) / v².
Reference Values
Use these tables as a sanity check on your result. Numbers are typical published muzzle figures and will vary with barrel length, load, and conditions.
| Cartridge / Projectile | Weight (gr) | Velocity (ft/s) | Energy (ft-lb) |
|---|---|---|---|
| .177 air pellet | 7.9 | 1,000 | 18 |
| .22 LR | 40 | 1,200 | 128 |
| Hunting arrow | 400 | 280 | 70 |
| 9mm Luger | 124 | 1,150 | 364 |
| .45 ACP | 230 | 850 | 369 |
| .357 Magnum | 125 | 1,450 | 584 |
| .223 Remington | 55 | 3,240 | 1,282 |
| .308 Winchester | 150 | 2,800 | 2,612 |
| .300 Win Mag | 180 | 2,960 | 3,503 |
| Energy Range (ft-lb) | Typical Class |
|---|---|
| Under 20 | Low-power airguns, light target pellets |
| 20 – 80 | Magnum airguns, bows, light arrows |
| 80 – 300 | Rimfire, heavy arrows, light handguns |
| 300 – 800 | Common centerfire handgun loads |
| 800 – 3,500 | Centerfire rifle loads |
| Over 3,500 | Magnum rifle and large dangerous-game loads |
Worked Examples and Common Questions
Example 1: 9mm 124 gr at 1,150 ft/s.
KE = (124 × 1,150²) / 450,436 = (124 × 1,322,500) / 450,436 = 163,990,000 / 450,436 = 364 ft-lb.
Example 2: .308 150 gr at 2,800 ft/s.
KE = (150 × 2,800²) / 450,436 = (150 × 7,840,000) / 450,436 = 1,176,000,000 / 450,436 = 2,611 ft-lb.
Example 3: Reverse solve. You want 500 ft-lb from a 230 gr projectile. Required velocity = sqrt(500 × 450,436 / 230) = sqrt(978,991) = 989 ft/s.
Why grains and ft/s? The conversion factor 450,436 bakes in the unit math so the answer comes out directly in ft-lb. If you used pounds and ft/s, the formula would be KE = (m × v²) / (2 × 32.174).
Does foot-pounds measure stopping power? No. Foot-pounds is kinetic energy at the muzzle or chronograph point. Terminal effect depends on bullet construction, expansion, penetration, and shot placement. Use ft-lb to compare loads, not to predict wound performance.
How accurate is the result? The formula is exact for the inputs you give it. Real-world accuracy depends on your velocity measurement. A 50 ft/s error on a 2,800 ft/s load shifts energy by roughly 90 ft-lb.
Converting to joules. Multiply ft-lb by 1.3558. So 364 ft-lb equals about 493 J. The calculator shows both values automatically.
Why does velocity matter more than weight? Energy scales with v². A 10% velocity increase raises energy about 21%. A 10% weight increase raises energy only 10%. That is why high-velocity rifle rounds outpace heavy but slow handgun rounds in ft-lb even with much lighter projectiles.
