# FPE Calculator – Foot-Pounds of Energy

URL: https://speedycalculator.com/calculators/physics/foot-pounds-of-energy/
Last updated: 2026-10-30

> The FPE calculator finds the foot-pounds of energy of a projectile – airgun pellet, arrow or bullet – from its velocity in ft/s and weight in grains.

## Inputs

- Velocity (ft/s, m/s, mph, km/h)
- Weight (gr, g, kg, oz)

## Results

- Foot-pounds of energy
- Momentum

## Formula

```
FPE = weight (gr) × velocity² (ft/s) / 450,240
```

## Explanation

Foot-pounds of energy (FPE) is how airgun and archery equipment is usually rated. Many countries set legal FPE limits for airguns, and hunters use FPE to match equipment to game.

### How to use the FPE Calculator – Foot-Pounds of Energy

- **Velocity**
- **Weight**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the velocity and the projectile weight in grains. The constant 450,240 combines the grains-to-pounds conversion, standard gravity and the ½ in the kinetic energy formula.

### Inputs explained

FieldWhat to enterVelocityUnits: ft/s, m/s, mph, km/hWeightUnits: gr, g, kg, oz

### What each result means

- **Foot-pounds of energy** = [Weight]×[Velocity]^2÷2
- **Momentum** = [Weight]×[Velocity]

### Example values

How the main result changes when **Velocity** changes and everything else stays at the example values above:

Velocity (ft/s)Foot-pounds of energy (ft·lbf)4506.42967514.46590025.7151,12540.181,35057.8591,800102.86

## Worked example

Inputs — Velocity: 900 ft/s; Weight: 14.3 gr.

Results — **Foot-pounds of energy = 25.715 ft·lbf**; Momentum = 0.25419 kg·m/s.

## Key terms

- **Foot-pound**: Energy to raise one pound by one foot.

## FAQ

**What is the UK legal limit for air rifles without a certificate?**
12 ft·lbf (6 ft·lbf for air pistols).

**How do I convert FPE to joules?**
Multiply by 1.3558.

**Why 450,240?**
It equals 2 × 32.16 × 7,000 (an older rounded g) – gravity times grains per pound times two.

**Does a heavier pellet give more FPE?**
Often slightly, at a lower velocity.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)