Calculate projectile foot-pounds and joules from weight and velocity, or reverse-solve the velocity or weight needed for a target energy.

Use mass and measured speed at the same point.

Classical kinetic-energy arithmetic. Energy alone does not determine terminal effects, equipment suitability or legal compliance.

FPE Formula

FPE = (massgrains × speedfps²) / 450436.679790026
  • FPE — kinetic energy in foot-pounds (ft-lbs)
  • mass_grains — projectile mass in grains (7000 grains = 1 lb)
  • speed_fps — projectile velocity in feet per second
  • 450436.679790026 — approximate divisor derived from the exact SI mass, length and foot-pound-force conversions

The other modes use:

Momentum (kg·m / s) = massgrains × 0.00006479891 × speedfps × 0.3048
Velocityfps = sqrt((FPE × 450436.679790026) / massgrains)

FPE is kinetic energy at the supplied speed. It is muzzle energy only when muzzle speed is entered. The calculator does not model drag or downrange speed. It uses E = ½mv² in SI units and converts with 1 ft·lbf = 1.3558179483314004 J.

Reference Values

Illustrative mass/speed pairs and their approximate classical energies; these are not verified product performance specifications:

Cartridge / Pellet Weight Velocity FPE
.177 airgun example8 gr820 fps~12 ft-lbs
.22 airgun (PCP)14.3 gr900 fps~26 ft-lbs
.22 LR40 gr1080 fps~104 ft-lbs
9mm Luger124 gr1150 fps~364 ft-lbs
.223 Rem55 gr3240 fps~1282 ft-lbs
.308 Win150 gr2800 fps~2611 ft-lbs
Hunting arrow500 gr280 fps~87 ft-lbs

Energy alone does not establish legal status, safe equipment use or suitability for a purpose. The calculator does not evaluate a jurisdiction’s rules or recommend hunting-energy thresholds.

Worked Example

A 124 gr 9mm bullet leaves the muzzle at 1150 fps:

FPE = (124 × 1150²) / 450436.679790026 ≈ 364.1 ft·lbf

Why use 450436.679790026? Standard kinetic energy is ½mv². Convert grains to kilograms (0.00006479891 kg per grain) and feet to meters (0.3048 m per foot), calculate joules, then divide by 1.3558179483314004 J per ft·lbf. This gives an equivalent divisor of approximately 450436.679790026; it replaces the older rounded450240 convention.

FPE vs. momentum: At a fixed mass, kinetic energy scales with speed squared while momentum scales linearly with speed. At a fixed speed, both scale linearly with mass. Neither number alone predicts terminal effects.

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.