Who needs this?
If you own a chronograph or play where one is used, you'll run into this:
- Airsoft playersThe field chronos your gun with 0.20 g BBs, but you shoot 0.28 g. Does it still pass?
- Paintball playersMarkers are tested in fps, and you want to know what 280 fps actually means in energy.
- Airgun shootersPellet tins list weight in grains, the chronograph reads fps, and the spec sheet quotes foot-pounds.
- Field and club staffRules written in joules have to be checked with a chronograph that only measures speed.
- Physics studentsKinetic energy is the classic first example of why squaring a number changes everything.
- Curious readersWhy does a tiny pellet sting so much more than a paintball that carries less energy?
Why speed counts twice
A moving object carries energy in proportion to its mass and to its speed squared. Think of a hammer: a heavier one hits harder, but swinging the same hammer twice as fast hits four times as hard.
- Double the mass at the same speed and the energy doubles.
- Double the speed with the same mass and the energy goes up four times.
- 10% more speed gives about 21% more energy (1.1² = 1.21), while 10% more mass gives exactly 10% more.
The SI unit is the joule (J). US airgun makers often use the foot-pound (ft·lbf), the energy needed to lift one pound by one foot. One foot-pound is 1.3558 J.
Doing the math, step by step
The formula only works in SI units: mass in kilograms, speed in meters per second. The answer then comes out in joules. Here's the 0.20 g BB at 350 fps:
- Grams to kilograms
0.20 g ÷ 1,000 = 0.0002 kg - fps to m/s (× 0.3048)
350 × 0.3048 = 106.68 m/s - Square the speed
106.68² = 11,380.6 - Multiply by ½ × mass
0.5 × 0.0002 × 11,380.6 = 1.14 J - Joules to foot-pounds
1.14 ÷ 1.3558 = 0.84 ft·lbf
Pellets are sold by the grain (gr), exactly 64.79891 milligrams, so an 8.2 grain .177 pellet is 0.531 g. The calculator takes grams or grains and fps or m/s, so you can type numbers straight off the tin and the chronograph.
Projectile mass: 0.2 gMuzzle velocity: 350 fpsDiameter: 6 mmDistance to target: 10 mDrag coefficient: 0.47
To move between joules and foot-pounds on their own:
Real situations, worked out
0.5 × 0.0002 kg × (106.68 m/s)² = 1.138 J, or 0.84 ft·lbf.
0.20 g at 350 fps ≈ 1.14 JSpeed comes from rearranging the formula: v = √(2E ÷ m) = √(2 × 1.138 ÷ 0.00028) = 90.16 m/s, or about 296 fps. Slower, same energy. That's why many fields set limits in joules, or name the BB weight for the chrono, instead of quoting fps alone.
0.28 g at about 296 fps ≈ 1.14 JA 0.53 g (about 8.2 grain) pellet: 900 × 0.3048 = 274.32 m/s, and 0.5 × 0.00053 × 274.32² = 19.94 J, or 14.71 ft·lbf. That's about 17 times the energy of the airsoft BB above, mostly because the speed is about 2.6 times higher.
0.53 g at 900 fps ≈ 19.9 J (14.7 ft·lbf)Projectile mass: 0.53 gMuzzle velocity: 900 fpsDiameter: 4.5 mmDistance to target: 0 mDrag coefficient: 0.47
A 3.2 g .68 paintball at 280 fps carries 11.65 J spread over a 2.34 cm² face: about 5.0 J/cm². Put the same 11.65 J behind a .177 pellet (0.159 cm² face) and it's about 73 J/cm², nearly 15 times as concentrated. That's why a small pellet breaks skin where a paintball with the same energy leaves a welt. Energy density is the figure penetration studies compare, and the calculator shows it.
Same 11.65 J: 5.0 J/cm² (paintball) vs 73 J/cm² (pellet)Energy at the target is lower
Drag slows a projectile from the moment it leaves the barrel, and since energy follows speed squared, energy drops faster than speed. The calculator uses a constant drag coefficient (0.47 for a smooth sphere) in sea-level air. In that model the 0.20 g BB above is down to about 233 fps at 10 m, leaving 0.50 J, less than half its muzzle energy. Drop ignores hop-up spin, so treat it as rough for airsoft.
Doing it in your head
For a quick estimate: multiply grams by (fps ÷ 100)², then halve it. A 0.20 g BB at 350 fps: 0.20 × 3.5² = 2.45, halved is 1.23 J. The rule always runs about 8% high (the exact factor is 0.4645 instead of 0.5), which errs on the cautious side.
For airgunners working in grains, the standard shortcut is ft·lbf = grains × fps² ÷ 450,437. An 8.18 grain pellet at 900 fps: 8.18 × 810,000 ÷ 450,437 = 14.7 ft·lbf.
It also helps to know which speed matches a given energy for each BB weight. All of these carry 1.14 J:
| BB weight | Speed for 1.14 J |
|---|---|
| 0.12 g | 452 fps |
| 0.20 g | 350 fps |
| 0.25 g | 313 fps |
| 0.28 g | 296 fps |
| 0.30 g | 286 fps |
| 0.32 g | 277 fps |
Speed falls with the square root of mass, so a BB 40% heavier only needs to be about 15% slower for the same energy.
Common mistakes
Mixing up grams and grains. One gram is 15.43 grains. Type an 8.2 grain pellet in as 8.2 g and the energy comes out more than 15 times too high. Check the unit menu before you trust the answer.
Comparing fps across different BB weights. 350 fps with 0.20 g BBs (1.14 J) and 350 fps with 0.28 g BBs (1.59 J) are different energies. A chronograph reading only means something alongside the weight it was taken with.
Treating muzzle energy as impact energy. The chronograph measures speed at the muzzle. At 10 or 20 m the projectile has slowed, and the energy has dropped even more. Set a distance in the calculator to see by how much.
Reading the impact bands as an eye-safety rating. The calculator's bands (under 60 J, 60–85, 85–200, over 200) are a simplified guide to blunt impact on the body, used for less-lethal launchers. They don't apply to eyes: any BB, pellet or paintball can blind, so always wear rated eye protection.
A bit of history
- 1686Gottfried Wilhelm Leibniz argues that the "living force" (vis viva) of a moving body is mass times speed squared, starting a long dispute with followers of Descartes, who used mass times speed.
- 1722Willem 's Gravesande drops brass balls into soft clay. A ball dropped from four times the height, hitting twice as fast, sinks four times as deep, which supports Leibniz.
- 1742Benjamin Robins publishes New Principles of Gunnery, describing the ballistic pendulum, the first practical way to measure a bullet's speed.
- 1829Gaspard-Gustave Coriolis adds the factor of ½, giving the formula used today, ½mv².
- c. 1849William Thomson, later Lord Kelvin, coins the term "kinetic energy."
Reference table
Example setups, matching the calculator's reference list. These aren't field or legal limits: rules vary by field, club and place, so check before you play.
| Setup | Mass | Speed | Energy | Foot-pounds |
|---|---|---|---|---|
| Airsoft BB | 0.20 g | 350 fps | 1.14 J | 0.84 |
| Airsoft BB | 0.28 g | 400 fps | 2.08 J | 1.53 |
| .68 paintball | 3.2 g | 280 fps | 11.7 J | 8.60 |
| .50 paintball | 1.2 g | 280 fps | 4.37 J | 3.22 |
| .177 pellet | 0.53 g | 900 fps | 19.9 J | 14.7 |
| .22 pellet | 0.93 g | 700 fps | 21.2 J | 15.6 |
Questions people ask
How many joules is 350 fps?
It depends on the weight: 1.14 J with a 0.20 g BB, 1.42 J with 0.25 g and 1.59 J with 0.28 g.
How do I convert joules to foot-pounds?
Divide by 1.3558. To go the other way, multiply foot-pounds by 1.3558. 20 J is about 14.75 ft·lbf.
Does a heavier BB hit harder?
At the same muzzle energy, a heavier BB starts slower but holds its speed better. In the calculator's model, a 0.28 g BB keeps 0.64 J at 10 m against 0.50 J for a 0.20 g BB that started with the same 1.14 J.
What's the 450,437 in the airgun formula?
It folds the unit conversions and the ½ into one number. Some older references use 450,240; the difference is under 0.05%.