FPE Calculator

What FPE measures

FPE stands for foot-pounds of energy, and it is the kinetic energy of a moving projectile written in the foot-pound, the energy unit of the US customary system. One foot-pound is the work done lifting one pound through one foot. A projectile in flight carries energy because it is moving, and the amount is fixed by two numbers only: how heavy it is and how fast it goes. Weight enters once, speed enters squared, which is why a modest change in speed moves the energy more than the same change in weight.

The physics version of the formula is kinetic energy equals one half mass times velocity squared. Ballistics shortcuts fold the unit conversions into a single constant so you can use the numbers printed on the box: FPE = grains x fps squared / 450,240. The exact constant, worked out through SI units, is 450,436.7, so the shortcut runs about 0.04 percent high. On a 150 grain bullet at 2,900 fps the shortcut reads 2,801.8 ft-lb against an exact 2,800.6 ft-lb, a gap smaller than the difference between two shots from the same rifle. Both constants come from the same definitions the NIST Guide to the SI, Appendix B.9 lists for the grain and the foot-pound-force (NIST, 2008).

Common loads at a glance

Typical factory velocities, computed with the same formula. Treat them as illustrations, since real loads vary by maker.

The units the formula expects

The shortcut exists because ammunition and airgun pellets are weighed in grains and speeds are quoted in feet per second. A grain is defined as 1/7000 of a pound, which the NIST guide fixes at 64.79891 milligrams. That is a small unit on purpose: a .22 pellet weighs 14.3 grains, a bit under one gram, and grains let you write it as a whole number instead of 0.0009 ounces. Chronographs read feet per second because that is the unit shooters and hunters already use for distance.

Speeds convert at 1 fps = 0.3048 m/s exactly, so 2,900 fps is 884 m/s and 800 fps is 244 m/s. If your data sheet gives meters per second or miles per hour, the calculator accepts those too and does the conversion before touching the formula. Mixing units is the single most common way to get an answer off by a factor of ten or more, so check the two unit menus before checking anything else.

Worked example: a 150 grain bullet at 2,900 fps

Take a common mid-weight deer bullet. Weight: 150 grains, which is 150/7000 = 0.0214 lb, or 0.009720 kg. Speed: 2,900 fps, which is 883.9 m/s. Kinetic energy is 0.5 x 0.009720 x 883.9 squared = 3,797 joules, and 3,797 / 1.355818 = 2,800.6 ft-lb. The calculator reports the same two figures plus the momentum, 62.1 lb-ft/s, and the power factor, 150 x 2900 / 1000 = 435.

Now swap the bullet. A 55 grain varmint round at 3,240 fps carries 1,281.8 ft-lb. The light bullet leaves 340 fps faster and still carries less than half the energy, because 150 grains is 2.7 times the weight and the extra speed cannot make up for it. That trade is the whole reason bullet weight exists as a choice.

The squared term is easy to feel on a pellet. Set the weight at 14.3 grains and read the ladder the calculator prints underneath the result: 640 fps gives 13.0 ft-lb, 800 fps gives 20.3 ft-lb, and 960 fps gives 29.3 ft-lb. Raising the speed 20 percent raised the energy 44 percent, and the same pellet twice as fast would carry four times the energy.

Running the formula backwards

Two of the three inputs are sometimes the question instead of the data. If a rule or a target figure sets the energy, the calculator solves for the missing one.

Speed from a target: you want 1,000 ft-lb from a 180 grain bullet. Rearranged, speed = sqrt(target x 450,436.7 / weight) = sqrt(1,000 x 450,436.7 / 180) = sqrt(2,502,426) = 1,582 fps. Any load slower than that misses the figure with this bullet weight, no matter what the advertising says.

Weight from a target: you want 215 ft-lb at 800 fps. Weight = target x 450,436.7 / speed squared = 215 x 450,436.7 / 640,000 = 151.3 grains. A 150 grain pellet at the same speed gives 213.1 ft-lb, which is why 1.3 grains of weight is worth noticing when a rule draws a line at a number.

Where the number is used as a legal line

Wildlife agencies use muzzle energy because it is a number anyone can compute from the box. Texas writes its airgun rule in both units: for the 2026 through 2027 seasons, pre-charged pneumatic air guns used on deer, pronghorn, wild turkey and other game must fire a projectile of at least .30 caliber and at least 150 grains, with a minimum muzzle velocity of 800 fps, or any combination that produces at least 215 foot-pounds at the muzzle, per the Texas Parks and Wildlife means and methods rules (TPWD, 2026).

South Dakota sets minimums for firearms. The state's 2026 big game regulations require at least 1,000 foot-pounds at the muzzle for shoulder-held firearms used on deer and antelope, at least 500 foot-pounds for handguns, and for elk both a caliber of at least .243 and at least 1,700 foot-pounds, a floor the administrative rule 41:06:04:13 has carried since 1993 (amended 2020).

Two cautions before treating these as your own numbers. Agencies phrase the requirements differently, some as velocity floors and some as energy floors, and the Texas example shows the two paths are not the same: 150 grains at 800 fps clears the velocity test at 213.1 ft-lb without clearing an energy test at 215. Second, most of these figures are muzzle values, and energy drops along the flight, so a load that qualifies at the muzzle may fall below a rule written at 100 yards. Check the current regulation for the state you hunt in before relying on any figure here.

What energy does and does not tell you

Energy is a measure of capacity, not of outcome. Two projectiles with the same foot-pounds can behave nothing alike, because energy says nothing about how the projectile is shaped, how it expands, or how deep it drives. Comparisons stay honest only within one family of projectiles.

Momentum is the companion figure, and it weights mass more and speed less. The 400 grain arrow at 300 fps in the calculator carries 79.9 ft-lb, less than a tenth of the 150 grain rifle round's 2,800.6 ft-lb, yet its momentum is 17.1 lb-ft/s against the bullet's 62.1. Heavy and slow keeps a bigger share of its momentum than light and fast at equal energy, which is why archers read both numbers. The same logic splits the light-fast and heavy-slow schools of bullet selection.

The second limit is distance. The formula gives the energy at the point where the speed was measured, which for a chronograph is the muzzle or a few feet past it. Downrange, drag bleeds speed off, and light projectiles bleed faster than heavy ones of the same shape. Predicting a 100 yard figure needs the ballistic coefficient and an exterior ballistics model, which this page does not attempt. Treat a downrange claim from a load table as measured data and a downrange claim from a muzzle calculation as an overestimate.

How to read the calculator

The calculator has one set of inputs and three questions. In the default energy mode, enter a weight and a muzzle speed and read the foot-pounds, the joules, the momentum and the power factor. In speed mode, enter a weight and a target energy and it returns the muzzle velocity needed. In weight mode, enter a speed and a target energy and it returns the projectile weight needed. Under the results sits a ladder that shows the energy for the same projectile at 80, 90, 100, 110 and 120 percent of your speed, so the square law is visible rather than described.

Results come from the exact SI route, grains to kilograms and fps to meters per second, then joules to foot-pounds at 1.355818, and the table also shows what the 450,240 shortcut would have printed so you can see the gap, which is about 0.04 percent. Weights in grams and ounces convert at 15.432 grains to the gram and 437.5 grains to the ounce. If a result looks impossible, the usual culprit is the unit menu, a weight typed in grams while the menu still says grains, and the fastest check is whether the grains line matches what you meant to enter.