Bullet Kinetic Energy Calculator & Formula

This calculator works out the kinetic energy of a bullet in foot-pounds or joules from its mass and velocity. You enter the bullet weight in grains and the muzzle velocity in feet per second, and you get the kinetic energy, plus momentum as a useful secondary figure. The result is the standard physics formula KE = ½mv², applied to a projectile.

Formula

The kinetic energy of any moving object is KE = ½ × m × v², where m is mass and v is velocity. For bullets, mass is usually given in grains (gr) and velocity in feet per second (ft/s), so the formula becomes:

KE (ft-lb) = (weight in grains ÷ 7000) × (velocity in ft/s)² ÷ (2 × 32.174)

• weight – bullet mass in grains (1 lb = 7000 grains)
• velocity – bullet speed in feet per second
• 32.174 – standard gravity in ft/s², converts pound-mass to pound-force
• KE – kinetic energy in foot-pounds (ft-lb)

To get joules instead, multiply the ft-lb result by 1.3558. The same formula works with metric units directly: KE (J) = ½ × mass (kg) × velocity (m/s)².

Worked Example

Using the default values from the calculator – a 115-grain bullet at 1200 ft/s:

1. Convert grains to pounds: 115 ÷ 7000 = 0.01643 lb
2. Square the velocity: 1200² = 1,440,000
3. Multiply mass by velocity squared: 0.01643 × 1,440,000 = 23,657
4. Divide by 2 × 32.174: 23,657 ÷ 64.348 = 367.6 ft-lb

The calculator rounds this to 367.6 ft-lb. Momentum is (0.01643 × 1200) ÷ 32.174 = 0.613 lb·s.

Why Kinetic Energy Matters for Bullets

Kinetic energy is the most common single number used to compare cartridge power. It tells you how much work the bullet can do on a target, which relates to penetration and tissue disruption. However, it does not tell the whole story: bullet construction, sectional density, and expansion matter just as much. A light fast bullet and a heavy slow bullet can have identical energy but behave very differently on impact.

In practical terms, energy figures are used for:

• Comparing loads for hunting – many jurisdictions set minimum energy for certain game
• Estimating recoil – heavier bullets and higher velocities produce more felt recoil
• Understanding trajectory – energy drops as velocity decays downrange

Remember that the calculator gives muzzle energy unless you input a downrange velocity. Energy falls off quickly with distance; a bullet that starts at 1200 ft/s may have only 70% of its muzzle energy at 100 yards.

How to Use the Calculator Correctly

Enter the actual bullet weight from the box or reloading manual, not the cartridge name. For example, a 9mm Luger cartridge can have bullets from 115 to 147 grains. The velocity should be the muzzle velocity from the manufacturer or a chronograph reading. If you only have energy in joules, divide by 1.3558 to get ft-lb.

For metric users, convert: 1 grain = 0.0648 grams, 1 ft/s = 0.3048 m/s. The calculator assumes standard sea-level gravity; the error from altitude or latitude is negligible for practical purposes.

Common Mistakes and Misconceptions

The biggest mistake is mixing units – using grams with ft/s or grains with m/s. Always keep mass and velocity in the same system. Another common error is confusing momentum with energy. Momentum (mass × velocity) is a vector and is conserved in collisions; energy is scalar and is not conserved in inelastic impacts. A heavy bullet at low speed can have high momentum but low energy, which is why momentum is listed as a separate output.

A widespread misconception is that doubling velocity doubles energy. It actually quadruples it because velocity is squared. That’s why a small increase in speed can noticeably boost energy, and why high-velocity cartridges are often touted for flat trajectories.

Limitations of the Formula

The formula assumes the bullet is a rigid point mass moving in a vacuum. In reality, air resistance slows the bullet, so downrange energy is lower than muzzle energy. The formula also ignores rotational energy from spin, which is tiny (less than 0.1% of translational energy). For subsonic vs. supersonic flight, the energy formula itself doesn’t change, but the ballistic coefficient affects how quickly velocity drops.

Do not use kinetic energy alone to judge stopping power or safety. Terminal ballistics involve penetration depth, temporary cavity, and tissue damage – none of which are captured by a single energy number. For hunting, also consider bullet expansion and shot placement.

Frequently Asked Questions

What is a good kinetic energy for hunting?

Many hunters use rough guidelines like 1000 ft-lb for deer-sized game, but this varies widely by bullet type, shot distance, and local regulations. Check your local hunting laws for minimum energy requirements, and consult ballistic data for the specific cartridge and bullet you plan to use.

How does barrel length affect bullet energy?

Longer barrels allow more powder to burn before the bullet exits, increasing velocity and therefore energy. A 4-inch barrel may produce 100-200 ft/s less than a 6-inch barrel for the same cartridge. The calculator uses the velocity you enter, so use a chronograph or manufacturer data for your specific barrel length.

Is muzzle energy the same as recoil energy?

No. Recoil energy is the backward energy of the gun, calculated from the firearm’s weight and the bullet’s momentum (plus powder gas). A light bullet at high velocity can have high muzzle energy but lower recoil than a heavy bullet at moderate velocity, because momentum is lower.

Why do some cartridges have similar energy but different performance?

Because energy doesn’t account for bullet diameter, weight, or construction. A 45 ACP and a 9mm can have similar energy, but the 45 uses a heavier, larger bullet that penetrates differently. Sectional density and expansion are better predictors of terminal effect.

Can I use this calculator for air rifles or arrows?

Yes, the physics is the same. Enter the projectile weight in grains and its velocity in ft/s. For arrows, use the arrow’s total weight (including broadhead). The result will be in ft-lb, which is commonly used for airgun and crossbow energy.

Related

• Pulse Pressure: Formula, Calculation, and Meaning
• Calculate Pipe Velocity: Formula and Examples
• Calculate Gravity: Formula, Examples, and Earth’s Value

in weight | Bullet weight | grains | 115 | 0
in vel | Muzzle velocity | ft/s | 1200 | 0
out energy | Kinetic energy | ft-lb | (weight / 7000) * vel^2 / (2 * 32.174) | 1
out momentum | Momentum | lb·s | (weight / 7000) * vel / 32.174 | 3