What muzzle energy is, and where 450,240 comes from
Muzzle energy is ordinary kinetic energy, ½mv², expressed in the units the shooting world happens to use. The only reason it looks unfamiliar is that bullets are weighed in grains and clocked in feet per second, so the constants get folded together into a single divisor.
Work through it. A grain is 1/7,000 of a pound, and a pound is a force, not a mass, so it has to be divided by g to become a mass in slugs. Substituting into ½mv² gives E = w·v² / (2 × 7,000 × g). With g = 32.16 ft/s² that denominator is 450,240, which is the constant in every published ammunition table. The modern standard value of g is 32.174, which would give 450,436 — a difference of 0.04%, or about one foot-pound in a 2,700 ft-lb rifle load. This calculator uses 450,240 so its results match printed factory ballistics.
The important consequence is the square. Energy rises with the square of velocity but only linearly with weight, so a 10% velocity increase adds 21% of energy while a 10% weight increase adds 10%. That asymmetry drives almost every debate about cartridge selection, and it is also why energy figures fall away so quickly downrange: a bullet that has lost a quarter of its velocity has lost 44% of its energy.
Momentum, power factor, Taylor index and sectional density
Energy is one of four different single-number summaries on this page, and they disagree with each other on purpose.
Momentum is mv rather than ½mv², so it weights mass and velocity equally. In grain-foot-second units it is w·v/7,000, giving a figure in pound-feet per second. Momentum is what governs recoil and what a heavy, slow bullet has in abundance relative to its energy.
Power factor is the same product with a different divisor: w·v/1,000. Practical shooting bodies use it to equalise recoil between competitors rather than to measure effect on target, because a scoring system that ignored recoil would reward the lightest possible load. USPSA and IPSC both set a minor floor of 125, USPSA sets its major floor at 165 and IPSC at 170; verify against the rulebook edition governing your match, since divisional floors are revised from time to time.
The Taylor knockout index, w·v·d/7,000, was proposed by the ivory hunter John Taylor in the 1940s as a way of comparing large-bore rifles on dangerous game. It is momentum multiplied by bullet diameter, so it deliberately rewards frontal area in a way energy does not. It has no theoretical derivation and Taylor never claimed one; treat it as a comparative index within a class of cartridges, not a physical quantity.
Sectional density, w/(7,000·d²), is weight divided by frontal area and carries no velocity at all. It predicts penetration and it is the numerator of the ballistic coefficient: BC = SD divided by a form factor that describes shape. A .308 bullet of 168 grains has a sectional density of 0.253, and a heavier 220-grain bullet of the same diameter reaches 0.331, which is why heavy-for-calibre bullets both penetrate more and buck wind better.
Worked example: a 168-grain .308 at 2,700 fps
Take the standard match load: a 168-grain .308-inch bullet leaving the muzzle at 2,700 fps.
- Muzzle energy. 168 × 2,700² = 168 × 7,290,000 = 1,224,720,000. Divide by 450,240: 2,720.1 ft-lb.
- In joules. 2,720.1 × 1.35582 = 3,688.0 J.
- Momentum. 168 × 2,700 / 7,000 = 453,600 / 7,000 = 64.80 lb·ft/s.
- Power factor. 168 × 2,700 / 1,000 = 453.6, far above any practical-shooting floor, as a rifle load should be.
- Taylor KO index. 168 × 2,700 × 0.308 / 7,000 = 139,708.8 / 7,000 = 19.96.
- Sectional density. 168 / (7,000 × 0.308²) = 168 / (7,000 × 0.094864) = 168 / 664.05 = 0.2530.
Now take the same bullet at 2,100 fps, roughly what it retains at 300 yards. Energy is 168 × 4,410,000 / 450,240 = 1,645.5 ft-lb, which is 60.5% of the muzzle figure. Velocity fell 22.2% and energy fell 39.5%, because 0.778² = 0.605. Momentum, by contrast, fell exactly 22.2% to 50.4 lb·ft/s. That divergence is the clearest demonstration of why the choice of metric changes the conclusion. To find the retained velocity at a given distance in the first place, use the bullet drop and trajectory calculator.
How much energy is enough
Energy thresholds circulate widely as hunting rules of thumb — often 1,000 ft-lb for deer and 1,500 for elk — and they are worth understanding as conventions rather than physics. No mechanism converts foot-pounds into a clean kill. What actually matters is that the bullet reaches the vitals and expands, and both of those depend on impact velocity and bullet construction, not on the energy number. Many jurisdictions do write minimum energy or minimum calibre into hunting regulations, so check the rules where you hunt; those are legal thresholds and they are binding regardless of what the ballistics say.
The number to watch instead is the minimum expansion velocity of the specific bullet you are shooting. Controlled-expansion designs commonly need somewhere around 1,800 to 2,000 fps to open reliably, while soft cup-and-core bullets and dedicated low-velocity designs work considerably lower. Manufacturers publish these figures for their own bullets; use theirs rather than a general rule. A bullet arriving with 1,200 ft-lb but below its expansion threshold will behave like a solid.
For competition, power factor is a pass-or-fail number checked at the chronograph, and the sample is your actual ammunition in your actual gun on the day. Load to clear the floor with margin, because temperature, barrel length and lot variation all move velocity by tens of feet per second, and a load that makes 168 in the shop can miss 165 on a cold morning.
For recoil comparison, momentum is the right metric, not energy. Free recoil velocity of the gun is bullet momentum plus a propellant-gas term divided by gun mass, so two loads with matching power factors kick similarly from the same gun regardless of their very different energies.
Muzzle energy of common cartridges
| Cartridge | Bullet (gr) | Velocity (fps) | Energy (ft-lb) | Energy (J) | Power factor |
|---|---|---|---|---|---|
| .22 LR | 40 | 1,255 | 140 | 190 | 50.2 |
| 9×19 mm | 115 | 1,180 | 356 | 482 | 135.7 |
| .45 ACP | 230 | 850 | 369 | 500 | 195.5 |
| .223 Rem | 55 | 3,240 | 1,282 | 1,738 | 178.2 |
| 7.62×39 mm | 123 | 2,350 | 1,509 | 2,046 | 289.1 |
| .308 Win | 168 | 2,700 | 2,720 | 3,688 | 453.6 |
| .30-06 Sprg | 180 | 2,700 | 2,914 | 3,951 | 486.0 |
| .300 Win Mag | 180 | 2,960 | 3,503 | 4,749 | 532.8 |
| .338 Lapua Mag | 250 | 2,950 | 4,832 | 6,552 | 737.5 |
| 12 ga slug (1 oz) | 437.5 | 1,600 | 2,488 | 3,373 | 700.0 |
Reproduce any row by entering its weight and velocity above. Velocities are nominal test-barrel figures of the kind SAAMI and CIP protocols produce; your own chronograph will differ.
Ways these numbers get misused
- Comparing energy across wildly different bullet types. A 4,800 ft-lb magnum and a 4,800 ft-lb slug load do entirely different things on impact, because construction and impact velocity govern behaviour, not the joule count.
- Using box velocity. Factory figures come from test barrels that are often longer than a hunting rifle's. A four-inch shorter barrel can cost 100 fps, which is roughly 7% of the energy.
- Quoting muzzle energy for a shot at distance. The relevant number is energy at impact. Compute the retained velocity first, then square it.
- Treating the Taylor index as physics. It is an empirical comparative index for large-bore rifles with no derivation behind it, and it deliberately favours diameter.
- Loading to exactly the power-factor floor. Chronograph variation, temperature and lot changes routinely move velocity by 20-40 fps. Build in margin or risk being scored minor.
- Confusing sectional density with ballistic coefficient. Sectional density ignores shape entirely; BC is sectional density divided by a form factor. Two bullets with identical SD can have very different drag.
Related calculations and where energy fits
Muzzle energy is the starting point of a chain. The bullet drop and trajectory calculator tells you what velocity survives to a given distance, which is the input this page needs for a meaningful downrange energy figure. The MOA and mil scope adjustment calculator handles the aiming correction for that same shot. Together the three cover the interior boundary conditions, the exterior flight and the sighting arithmetic.
Interior ballistics — how pressure and burn rate produce the muzzle velocity in the first place — is not covered here and should not be estimated. Use published load data from a powder or bullet manufacturer, and work up from the starting charge with a chronograph. Terminal ballistics, the behaviour of the bullet in the target, is likewise a domain of testing rather than of formulas; energy is a poor proxy for it, which is why bullet makers publish expansion velocity windows instead.
One genuinely useful application of the energy figure is comparing loads on the same axis. If you know two loads' weights and velocities, this page tells you which carries more energy, more momentum and more power factor, and the three answers will not always agree. That disagreement is informative: it tells you the loads differ in the mass-velocity trade, which is exactly the choice you are making when you pick between a light fast bullet and a heavy slow one.