acalculator

What is the muzzle energy?

Type the bullet weight and the muzzle velocity. The muzzle energy calculator works out the kinetic energy in foot-pounds and joules; fill the energy instead to find the velocity or the weight.

Your numbers

Units
Muzzle energy
2,648.23 ft·lbf

A 150 gr bullet at 2,820 ft/s has a muzzle energy of 2,648.23 ft·lbf.

Energy in foot-poundsft·lbf
2,648.2
Energy in joulesJ
3,590.5
MomentumN·s
8.355

Muzzle energy: 2,648.23 ft·lbf. A 150 gr bullet at 2,820 ft/s has a muzzle energy of 2,648.23 ft·lbf.

How to calculate

Computes the muzzle energy of a bullet from its weight and muzzle velocity (E = ½mv²) in foot-pounds and joules, or the velocity or weight from the energy, with the momentum.

Example with the default inputs (Bullet weight 150 gr, Muzzle velocity 2,820 ft/s): A 150 gr bullet at 2,820 ft/s has a muzzle energy of 2,648.23 ft·lbf.

Formula: E = ½ × m × v²; m = 2E ÷ v²; v = √(2E ÷ m); momentum = m × v.

  • The energy is the kinetic energy of the bullet alone at the muzzle; spin and the powder gases are left out.
  • Units are converted exactly: 1 grain = 64.79891 mg, 1 ft = 0.3048 m, 1 ft·lbf = 1.3558179483314004 J (NIST SP 811).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Bullet weight 150 gr, Muzzle velocity 2,820 ft/s gives Muzzle energy 2,648.23 ft·lbf, Energy in foot-pounds 2,648.230159, Momentum 8.354549.Source: OpenStax University Physics Volume 1, section 7.2, Kinetic Energy, K = ½mv² (https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy, retrieved 2026-10-01); NIST SP 811 (1 gr = 64.79891 mg, 1 ft·lbf = 1.3558179483314004 J)
  2. Bullet weight 1,234,589 gr, Muzzle velocity 32.81 ft/s gives Muzzle energy 2,950.25 ft·lbf.Source: OpenStax University Physics Volume 1, section 7.2, Kinetic Energy, example: 80 kg at 10 m/s is 4.0 kJ (https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy)
  3. Bullet weight 55 gr, Muzzle energy 1,282 ft·lbf gives Muzzle velocity 3,240 ft/s.Source: NIST SP 811 units

How it works

Fill any two of bullet weight, muzzle velocity and muzzle energy, and leave one empty. With m the mass, v the velocity and E the energy:

  • E = ½ × m × v²
  • m = 2 × E ÷ v²
  • v = √(2 × E ÷ m)

The calculator converts every value to SI units first (kilograms, metres per second, joules), solves, and then shows:

  • Muzzle energy in foot-pounds (US) or joules (Metric), to 6 significant figures.
  • Bullet weight and muzzle velocity, when solved, in the unit of their box: to 4 significant figures, but whole units are never rounded away (a solved velocity of 3,240.26 ft/s shows as 3,240 ft/s; 865.277 shows as 865.3).
  • Energy in foot-pounds: joules ÷ 1.3558179483314004, to 1 decimal.
  • Energy in joules, to 1 decimal.
  • Momentum: m × v in newton-seconds (kg·m/s), to 4 significant figures.

Values are rounded half up for display only.

Rules

  • The bullet weight is more than 0 and at most 100 kg (1,543,236 grains), so a shell or the textbook’s 80 kg athlete fits too.
  • The velocity is more than 0 and at most 3,000 m/s (9,843 ft/s).
  • The energy is more than 0 and at most 500,000,000 J.
  • A value solved outside these ranges gives no answer.
  • Unit conversions are exact: 1 grain = 64.79891 mg, 1 ft = 0.3048 m, 1 ft·lbf = 0.3048 × 4.4482216152605 J, 1 g = 0.001 kg, 1 oz = 28.349523125 g.

Worked examples by hand

A 150-grain bullet at 2,820 ft/s. m = 150 × 64.79891 mg = 0.0097198365 kg. v = 2,820 × 0.3048 = 859.536 m/s. E = ½ × 0.0097198365 × 859.536² = 3,590.518 J, which is 3,590.518 ÷ 1.3558179 = 2,648.23 ft·lbf. Momentum = 0.0097198365 × 859.536 = 8.355 N·s.

The textbook’s athlete. 80 kg at 10 m/s: E = ½ × 80 × 10² = 4,000 J.

A 55-grain bullet with 1,282 ft·lbf. E = 1,282 × 1.3558179 = 1,738.16 J; m = 55 × 64.79891 mg = 0.00356394 kg; v = √(2 × 1,738.16 ÷ 0.00356394) = 987.63 m/s, which is 3,240.26 ft/s.

Other questions people ask

How do I calculate muzzle energy?

Use the kinetic energy formula, E = ½ × m × v², with the mass in kilograms and the speed in metres per second to get joules. A 150-grain bullet (0.0097198 kg) at 2,820 ft/s (859.536 m/s) has ½ × 0.0097198 × 859.536² = 3,590.5 J, which is 2,648.2 ft·lbf.

What is the 450,240 formula?

A shortcut for US units: energy in ft·lbf ≈ grains × (ft/s)² ÷ 450,240. The exact divisor from the unit definitions is 2 × 7,000 × 9.80665 ÷ 0.3048 = 450,436.68, so the shortcut reads about 0.04% high. The calculator uses the exact unit sizes.

Does a heavier bullet or a faster bullet give more energy?

Speed counts more, because it is squared. Doubling the weight doubles the energy; doubling the velocity makes it four times as large.

How do I find the velocity from the energy?

Rearrange the formula: v = √(2E ÷ m). Fill the bullet weight and the energy and leave the velocity empty. A 55-grain bullet with 1,282 ft·lbf leaves the muzzle at about 3,240 ft/s (3,240.26 before rounding).

What is a grain?

A unit of mass: 1 grain is exactly 64.79891 milligrams, and 7,000 grains make 1 pound. Bullet weights are given in grains in the US.

Is muzzle energy the energy at the target?

No. It is the energy as the bullet leaves the barrel. Air drag slows the bullet, so the energy at a distant target is lower; that needs the bullet’s ballistic coefficient and a drag model.