# What is the muzzle energy?

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.

- Page: https://www.acalculator.org/physics/muzzle-energy-calculator
- JSON spec: https://www.acalculator.org/physics/muzzle-energy-calculator.json
- Version: 3fee43a648b8

## Default answer

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.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| m | Bullet weight | The mass of the bullet (the projectile alone, not the cartridge). |
| v | Muzzle velocity | The speed of the bullet as it leaves the muzzle. |
| e | Muzzle energy | The kinetic energy of the bullet at the muzzle. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| m | Bullet weight | The mass of the bullet (the projectile alone, not the cartridge). |
| v | Muzzle velocity | The speed of the bullet as it leaves the muzzle. |
| e | Muzzle energy | The kinetic energy at the muzzle, ½ × m × v². |
| ftlbf | Energy in foot-pounds | The energy in foot-pounds (ft·lbf): joules ÷ 1.355 817 948 331 400 4. |
| joules | Energy in joules | The energy in joules: ½ × kilograms × (metres per second)². |
| momentum | Momentum | The momentum of the bullet, m × v, in newton-seconds (kg·m/s). |

## Method

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

## Assumptions

- 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).

## Worked examples

1. m = 0.00972, v = 859.536 gives e = 3,590.51798, ftlbf = 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. m = 80, v = 10 gives e = 4,000. 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. m = 0.003564, e = 1,738.15861 gives v = 987.630526. Source: NIST SP 811 units.

## FAQ

### 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.

## Sources

- OpenStax, University Physics Volume 1, section 7.2, Kinetic Energy (K = ½mv²; example: 80 kg at 10 m/s is 4.0 kJ), CC BY 4.0, retrieved 2026-10-01. https://openstax.org/books/university-physics-volume-1/pages/7-2-kinetic-energy
- NIST Special Publication 811, Guide for the Use of the International System of Units, Appendix B.8 (grain = 64.79891 mg, foot = 0.3048 m, pound-force = 4.4482216152605 N), retrieved 2026-10-01. https://www.nist.gov/pml/special-publication-811