FPE Calculator (air gun foot-pounds of energy & UK 12 / 6 ft·lb limits)

Understanding the FPE calculator — concept and principle

Air gun power is usually described in foot-pounds of energy (FPE) at the muzzle. This calculator works out FPE and joules from pellet weight and speed, compares the result with the limits used in Great Britain (12 ft·lb for air rifles, 6 ft·lb for air pistols) and shows the highest speed this pellet could reach at that limit.

11.4 ft·lbf is 95 % of the 12 ft·lbf limit for air rifles in Great Britain.

How it is calculated

E (J) = ½ × m × v²

FPE = E ÷ 1.3558 ≈ grains × fps² ÷ 450,437

Speed at limit L: v = √(2 L ÷ m)

m is pellet mass in kg (1 grain = 64.79891 mg), v is speed in m/s (1 ft = 0.3048 m).
The limit is 12 ft·lbf for air rifles and 6 ft·lbf for air pistols in Great Britain.

The principle

A pellet's muzzle energy is its kinetic energy, half its mass times its speed squared. Because speed is squared, small changes in velocity change energy noticeably. The same air gun gives slightly different energy with heavier or lighter pellets, because the gun's air charge does not transfer energy equally well to every pellet. Rearranging the energy equation shows the maximum speed a given pellet can have while staying under a legal energy limit: heavier pellets must go slower.

Worked example

Default inputs: 8.44-grain pellet at 780 fps, air rifle.

Mass = 8.44 × 64.79891 mg = 0.5469 g; speed = 780 × 0.3048 = 237.7 m/s.
E = 0.5 × 0.0005469 × 237.7² = 15.46 J.
FPE = 15.46 ÷ 1.3558 = 11.4 ft·lbf (check: 8.44 × 780² ÷ 450,437 = 11.4).
UK limit = 12 ft·lbf, so this is 95% of the limit: Within the UK limit.
Speed at the limit with this pellet = √(2 × 16.27 ÷ 0.0005469) = 243.9 m/s = 800 fps.

Each point is the calculator re-run with only “Pellet speed” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Pellet speed	Muzzle energy (ft·lbf)
195	0.71
390	2.85
585	6.41
780	11.4
975	17.81
1,170	25.65
1,560	45.6

How to read the result

Where does your result fall?

Measure speed with a chronograph close to the muzzle and test several shots, because speed varies from shot to shot. Rules differ widely between countries, and many give limits in joules rather than foot-pounds, so check the law where you live. A result close to the limit leaves little margin for shot-to-shot variation or a change of pellet.

Common mistakes

Using the advertised velocity, often measured with very light pellets.
Testing with one pellet type and then shooting a different one.
Forgetting that energy rises with the square of speed.
Assuming UK limits apply in other countries.

Keep in mind: This is a physics calculation, not legal advice. Air weapons can cause serious injury; follow the laws where you live and handle them safely.

Frequently asked questions

What is the UK legal limit for an air rifle?

Above 12 ft·lb of muzzle energy an air rifle needs a firearm certificate in Great Britain; air pistols, above 6 ft·lb.

How do I convert FPE to joules?

Multiply by about 1.356; 12 ft·lb is about 16.3 J.

Why does a heavier pellet change the FPE?

The gun transfers energy differently to different pellets, so speed does not fall exactly in proportion.

How many shots should I chronograph?

Several, so you can see the average and the highest values.

Sources: The Firearms (Dangerous Air Weapons) Rules 1969 (SI 1969/47), rule 2 (legislation.gov.uk) · Kinetic energy ½mv²; 1 grain = 64.79891 mg, 1 ft·lbf = 1.3558179 J (NIST SP 811)

Checked 9 Nov 2026. The Firearms (Dangerous Air Weapons) Rules 1969 (SI 1969/47), rule 2: air pistol above 6 ft. lb., other air weapon above 12 ft. lb. kinetic energy at the muzzle (legislation.gov.uk). Kinetic energy ½mv² with 1 grain = 64.79891 mg and 1 ft·lbf = 1.3558179 J (standard values). Not legal advice.

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