Formula
Foot-pounds are grains times velocity squared, divided by 450,437. Momentum in pound-seconds is grains times velocity, divided by 225,218. Joules are foot-pounds times 1.35582. Taylor’s factor is grains times velocity times diameter in inches, divided by 7,000.
ft·lbf = grains × fps² / 450,437
lb·s = grains × fps / 225,218
J = ft·lbf × 1.35582
TKO = grains × fps × diameter / 7,000
450,437 is the ballistic constant. The arrow page divides by Easton’s 450,240. Do not compare the two pages as if they shared a formula. Grams and metres per second are converted with 1 grain = 0.06479891 g and 1 fps = 0.3048 m/s before the formula runs. Drop, drift, and velocity downrange are the ballistic calculator. This page is energy at one speed. Neither page gives a powder charge.
Worked examples
150 gr at 2,820 fps. 150 × 2,820² / 450,437 = 2,648 ft·lbf. Momentum is 150 × 2,820 / 225,218 = 1.88 lb·s. Joules are that energy times 1.35582.
40 gr at 1,200 fps. A typical .22 LR figure: 40 × 1,200² / 450,437 = 128 ft·lbf.
The same 150 gr bullet entered as grams. 150 grains is 9.72 g and 2,820 fps is 859.5 m/s. The page converts back to grains and feet per second, so the energy matches.
Reference
Energy at the velocities shown, using 450,437. Momentum uses 225,218.
| Load | ft·lbf | J | lb·s |
|---|---|---|---|
| 40 gr, 1,200 fps | 128 | 173 | 0.21 |
| 55 gr, 3,240 fps | 1,282 | 1,738 | 0.79 |
| 150 gr, 2,820 fps | 2,648 | 3,591 | 1.88 |
| 180 gr, 2,700 fps | 2,913 | 3,950 | 2.16 |
Questions
How much energy does a 150 grain bullet at 2,820 feet per second carry?
About 2,648 foot-pounds. Energy is grains times velocity squared, divided by 450,437. That constant is the common ballistic identity. The arrow calculator on this site uses Easton’s 450,240 instead, so the two pages will not match on the same numbers, on purpose.
What is the momentum?
Grains times feet per second, divided by 225,218. That divisor is about 7,000 × 32.174, which converts grains to slugs and divides by gravity so the result is in pound-seconds.
What is the Taylor KO factor?
Grains times velocity times diameter in inches, divided by 7,000. It is an optional comparison number, not a measure of wounding. Leave the diameter at 0 and the factor is left blank.
Sources
- Kinetic energy, foot-pounds = grains × fps² / 450,437. Momentum, pound-seconds = grains × fps / 225,218. 225,218 ≈ 7,000 × 32.174.
- Joules = ft·lbf × 1.35582. Taylor KO = grains × fps × diameter (in) / 7,000. The arrow calculator uses Easton’s 450,240 and is a different formula.