Calculate muzzle energy in ft-lbs and joules from bullet weight in grains and velocity in fps, or solve for the velocity or weight for a target energy.

Diameter and recoil model
Blank omits sectional density and the historical comparison index.

Blank omits free recoil. The model excludes supports, mechanisms and redirected gases.

Blank uses zero: projectile-only recoil. Supply a measured or independently justified gas contribution.

Muzzle Energy Formula

E = 1 / 2 × m × v²
  • E = kinetic energy at the muzzle (joules, then converted to ft·lbf)
  • m = bullet mass (kilograms)
  • v = muzzle velocity (meters per second)

The calculator converts your inputs to SI units, computes joules, then divides by 1.3558 to display ft·lbf. To get ft·lbf directly from grains and fps, the equivalent shortcut is E = (grains × fps²) ÷ 450,437.

The reverse modes use v = √(2E/m) and m = 2E/v² in SI units. The following are secondary comparison formulas:

PF = (grains × fps) / 1000
TKO = (grains × fps × caliberᵢn) / 7000

The conventional power factor and historical Taylor comparison index use grains, ft/s and inches. Neither establishes competition eligibility or terminal performance. Sectional density uses mass in pounds divided by diameter in inches squared. Optional free recoil uses projectile momentum plus a gas-momentum contribution you supply; blank gas momentum gives a projectile-only model and can underestimate actual recoil. All energy results ignore downrange drag.

Reference Tables

Illustrative mass-and-speed arithmetic examples, not specifications for any cartridge or ammunition loading data:

Cartridge Bullet Velocity Energy
.22 LR40 gr1080 fps~104 ft·lbf
9mm Luger124 gr1150 fps~364 ft·lbf
.45 ACP230 gr850 fps~369 ft·lbf
.223 Rem55 gr3240 fps~1282 ft·lbf
.308 Win150 gr2820 fps~2648 ft·lbf
.30-06180 gr2700 fps~2913 ft·lbf
.300 Win Mag180 gr2960 fps~3502 ft·lbf
.375 H&H300 gr2530 fps~4263 ft·lbf
.458 Win Mag500 gr2090 fps~4849 ft·lbf

No universal energy-only hunting threshold is assessed here. Muzzle energy alone does not determine terminal performance, safe ammunition or legal compliance.

Worked Example

A 150-grain .308 bullet leaves the muzzle at 2820 fps.

  1. Convert mass: 150 gr × 0.00006479891 = 0.0097198365 kg
  2. Convert velocity: 2820 fps × 0.3048 = 859.536 m/s
  3. Apply formula: E = 0.5 × 0.0097198365 × 859.536² ≈ 3590.518 J
  4. Convert to ft·lbf: 3590.518 ÷ 1.3558179483314 ≈ 2648.230 ft·lbf

Why velocity matters more than weight: energy scales with the square of velocity but only linearly with mass. Doubling velocity quadruples energy. Doubling bullet weight only doubles it.

Muzzle vs. impact energy: the calculator gives energy at the muzzle. Bullets shed velocity to drag, so impact energy at 200+ yards is meaningfully lower. Use a ballistic calculator with BC and range for downrange figures.