Bullet Energy Calculator (muzzle energy in ft·lbf & joules from grains and fps)

Understanding the bullet energy calculator — concept and principle

This calculator works out the kinetic energy and momentum of a projectile from its weight and velocity, the figures printed on ammunition boxes and in load manuals. It accepts grains or grams and feet or metres per second, and if you enter a downrange velocity it shows how much energy remains. Hunters and target shooters use it to compare loads.

Energy grows with the square of speed: 3,591 J at the muzzle.

How it is calculated

E = ½ × m × v²

p = m × v

m is mass in kg (1 grain = 64.79891 mg; 7,000 grains = 1 lb), v is velocity in m/s (1 ft = 0.3048 m).
Energy in joules is converted to foot-pounds with 1 ft·lbf = 1.3558 J; in US units E ≈ grains × fps² ÷ 450,437.
Momentum is shown in N·s and lbf·s (1 lbf = 4.4482 N).
Energy kept downrange = Edownrange ÷ Emuzzle × 100 %.

The principle

Kinetic energy is the work needed to bring a mass up to a given speed, and it rises with the square of the speed. Doubling the weight of a projectile doubles its energy, but doubling its speed quadruples it. Momentum rises only in proportion to speed, so it describes how hard the projectile is to stop rather than how much work it can do. Air drag slows the projectile after it leaves the muzzle, and because energy depends on v², energy falls faster than velocity: keeping 80 % of the speed means keeping only 64 % of the energy.

Worked example

Default inputs: 150 grains at 2,820 fps, no downrange velocity.

Mass = 150 × 64.79891 mg = 9.72 g = 0.009720 kg.
Velocity = 2,820 × 0.3048 = 860 m/s (859.5 m/s).
E = 0.5 × 0.009720 × 859.5² = 3,591 J.
In foot-pounds: 3,591 ÷ 1.3558 = 2,648 ft·lbf (check: 150 × 2,820² ÷ 450,437 = 2,648).
Momentum = 0.009720 × 859.5 = 8.35 N·s = 1.878 lbf·s.
With no downrange velocity entered, the downrange rows show —.

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

Muzzle velocity	Muzzle energy (ft·lbf)
705	166
1,410	662
2,115	1,490
2,820	2,648
3,525	4,138
4,230	5,959
5,640	10,593

How to read the result

Muzzle energy is a convenient way to compare cartridges, but it is not the whole story: bullet construction, shot placement and the velocity at the target matter a great deal for hunting. Some jurisdictions set minimum energy or calibre rules for hunting certain game, so check your local regulations. Published velocities come from test barrels and may differ from your firearm because of barrel length and temperature; a chronograph gives your own figure.

Common mistakes

Mixing grains and grams; 150 grains is about 9.7 g, not 150 g.
Using the box velocity for a much shorter barrel.
Comparing energy alone and ignoring momentum and bullet design.
Forgetting that energy downrange drops faster than velocity.

Keep in mind: This is a physics calculation only. Firearm and ammunition use must follow local laws and safe handling practice; never exceed published load data.

Frequently asked questions

How do I convert grains to grams?

Multiply by 0.0648; 150 grains is about 9.72 g.

Why does speed matter more than weight for energy?

Energy depends on the square of speed but only linearly on mass.

What is the 450,437 constant?

It combines the unit conversions so that grains × fps² ÷ 450,437 gives foot-pounds.

Sources: Standard mechanics: kinetic energy ½mv² and momentum mv; exact units 1 grain = 64.79891 mg, 1 ft = 0.3048 m, 1 lbf = 4.4482216152605 N (NIST SP 811)

Checked 9 Nov 2026. Kinetic energy ½mv² and momentum mv (standard mechanics); exact unit definitions 1 grain = 64.79891 mg, 1 ft = 0.3048 m, 1 lbf = 4.4482216152605 N (standard values).

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