Foot-Pounds of Energy Calculator

Find foot-pounds of energy for any projectile.

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Foot-pounds of energy

KE = ½ × m × v²

Instructions — Foot-Pounds of Energy Calculator

  1. Enter projectile mass and pick a unit — grains, grams, ounces, or pounds.
  2. Enter velocity and pick a unit — ft/s (fps), m/s, mph, or km/h.
  3. Read kinetic energy in foot-pounds plus joules, calories, and unit-converted mass and velocity.
  4. Use a preset for common cartridges, an arrow, or a baseball if you want a quick benchmark.

Formulas

SI form (mass in kg, velocity in m/s, energy in joules):

$$KE = \tfrac{1}{2} m v^2$$

Imperial shortcut for bullets (mass in grains, velocity in fps, energy in foot-pounds):

$$KE_{\text{ft-lb}} = \frac{m_{gr} \times v_{fps}^2}{450{,}435}$$

Conversions: 1 ft·lb = 1.35582 J, 1 grain = 64.79891 mg, 1 fps = 0.3048 m/s.

Reference

  • 1 foot-pound = 1.35582 joules = 0.323833 calories
  • 9 mm Luger muzzle energy ≈ 364 ft·lb (494 J)
  • .308 Win muzzle energy ≈ 2,648 ft·lb (3,591 J)
  • .50 BMG muzzle energy ≈ 13,240 ft·lb (17,950 J)
  • Typical hunting arrow ≈ 65–80 ft·lb (88–108 J)
  • Major-league fastball ≈ 110 ft·lb (149 J) at 45 m/s
  • Deer hunting minimum impact: ~1,000 ft·lb
  • Elk/moose minimum impact: 1,500–2,000 ft·lb

Article — Foot-Pounds of Energy Calculator

Foot-pounds of energy calculator

Foot-pounds of energy is the kinetic energy of a moving projectile in imperial units, equal to ½mv² converted to ft·lb. A 124-grain 9mm bullet at 1,150 fps carries 364 ft·lb (494 J). A 350-grain hunting arrow at 290 fps carries about 65 ft·lb (88 J). One foot-pound equals 1.35582 joules.

Energy scales with the square of velocity, so a 10% velocity bump produces a 21% energy bump and doubling velocity quadruples energy. That single fact explains why short pistol barrels give up so much terminal energy, why arrow speed matters less than mass and why long-action rifle cartridges dominate at distance.

What is a foot-pound of energy?

A foot-pound (ft·lb) is the energy needed to lift a 1-pound weight one foot vertically in Earth's gravity, or the work done by a 1-pound force acting through 1 foot of distance. The metric equivalent is the joule. The conversion is 1 ft·lb = 1.35582 J, and 1 calorie = 4.184 J ≈ 3.086 ft·lb. The unit is most common in US ballistics, archery, automotive torque references (where it is technically pound-foot) and engineering carry-overs from the imperial system.

This calculator treats foot-pounds strictly as energy — the scalar quantity ½mv² for any moving object. Muzzle energy is the energy at the instant a bullet leaves the barrel; impact energy is what remains at the target. Air drag bleeds velocity along the way, and because energy scales with v², the energy drop downrange is steeper than the velocity drop.

Did you know

The Saturn V first stage at peak burn produced about 7.7 million pounds of thrust and an effective exhaust velocity of 2,580 m/s. The kinetic energy in the rocket exhaust over a one-second burn exceeded 18 billion foot-pounds — roughly the energy of 1.4 million 9mm bullets fired simultaneously.

The foot-pounds of energy formula

Two forms of the same physics. The SI textbook form uses kilograms and metres per second; the imperial shortcut wraps the conversions inside a single constant.

Foot-pounds of energy formulas
KE = ½mv² SI: kg, m/s → joules
KE (ft·lb) = (grains × fps²) / 450,435 imperial shortcut
1 ft·lb = 1.35582 J 1 J = 0.7376 ft·lb
1 grain = 64.79891 mg 1 fps = 0.3048 m/s

The 450,435 constant absorbs the conversion from grains to kilograms (divide by 15,432.36), the conversion from fps² to m²/s² (multiply by 0.3048²), the factor of one-half, and the conversion from joules back to foot-pounds. You do not have to derive it — but you do have to use grains and fps. Plug in pounds or mph and the answer is meaningless.

Foot-pounds by projectile type

Projectile energy spans more than four orders of magnitude in everyday contexts. Here are typical muzzle or release energies.

  • Airsoft 6mm BB (0.2 g, 100 m/s): 0.7 ft·lb (1 J). Recreational only.
  • BB gun (.177 pellet, 350 fps): 3–5 ft·lb (4–7 J). Backyard plinking.
  • Hunting arrow (350 gr, 290 fps): 65 ft·lb (88 J). Deer-legal in most states.
  • Crossbow bolt (400 gr, 380 fps): 128 ft·lb (174 J). Big-game range.
  • .22 LR (40 gr, 1,255 fps): 140 ft·lb (190 J). Small game and plinking.
  • 9 mm Luger (124 gr, 1,150 fps): 364 ft·lb (494 J). Standard handgun.
  • .308 Win (150 gr, 2,820 fps): 2,648 ft·lb (3,591 J). Hunting and military.
  • .50 BMG (750 gr, 2,820 fps): 13,240 ft·lb (17,950 J). Anti-materiel.
Arrow
65 ft·lb
350 gr @ 290 fps
9mm
364 ft·lb
124 gr @ 1,150 fps

Foot-pounds vs joules and calories

All three units measure energy, but they live in different worlds. Foot-pounds dominate US ballistics and mechanical engineering. Joules are the SI standard used in physics, chemistry and most non-US contexts. Calories — the food-energy unit — show up rarely in ballistics but matter when comparing projectile energy with biological energy.

A standard 12-ounce can of soda holds about 150 nutritional kilocalories (628 kJ, or 463,000 ft·lb). That single can stores more chemical energy than 35.50 BMG rounds carry as kinetic energy. The contrast highlights how slow chemical energy release is compared with the instantaneous transfer of bullet impact.

Foot-pounds of energy for hunting

State regulations and ethical guidelines often specify minimum kinetic energy thresholds at impact, not at the muzzle. The most common rules of thumb are 1,000 ft·lb for deer, 1,500 ft·lb for black bear and 1,800–2,500 ft·lb for elk, moose, or larger game.

Energy is necessary, not sufficient

A high foot-pound number does not guarantee a humane harvest. Bullet construction, sectional density, expansion behavior and shot placement matter at least as much. A heavy monolithic bullet at modest velocity can outperform a fragmenting bullet at higher energy on the same animal. Always pair the energy figure with appropriate bullet design and ethical range limits.

Downrange energy loss

Air drag bleeds velocity, and the v² term means energy drops faster than velocity. A bullet that retains 70% of muzzle velocity at 300 yards has only about 49% of its muzzle energy left. Ballistic coefficient (BC) measures aerodynamic efficiency: higher BC means a slower energy bleed.

  • 9mm at 100 yd: ~70% retained energy. Practical pistol range.
  • .308 Win at 300 yd: ~60% retained — still 1,500–1,700 ft·lb, deer-legal.
  • .308 Win at 600 yd: ~35% retained — drops below deer threshold for many.
  • .338 Lapua at 1,000 yd: ~35% retained — around 1,700 ft·lb.
  • Arrow at 40 yd: ~85% retained — arrows have very low drag relative to mass.

Common foot-pounds mistakes

Tip

Always check which energy you are quoting — muzzle, impact, or both. Manufacturer specs are typically muzzle energy; published hunting minimums are typically impact energy at the target range. The two can differ by 50% or more at typical hunting distances.

Beyond the muzzle-versus-impact mix-up, the second most common error is unit confusion. Pound-feet of torque (lbf·ft) describes a rotational force; foot-pounds of energy describes work or kinetic energy. They are written identically as ft·lb in everyday language, which leads people to compare engine torque numbers with bullet energy numbers as if they were the same quantity. They are not — engine torque is a force-times-distance per unit rotation; bullet energy is total mechanical work delivered.

The third trap is using foot-pounds as a single-number predictor of stopping power. FBI wound-ballistics research found that bullet placement and penetration depth dominate terminal performance. Two bullets with identical energy can produce very different outcomes if one expands reliably and the other does not, or if one is light-and-fast while the other is heavy-and-slow with greater sectional density.

FAQ

A foot-pound (ft·lb) is the energy needed to lift a 1-pound weight one foot vertically against gravity, or equivalently the work done by a 1-pound force acting through 1 foot of distance. As an SI conversion, 1 ft·lb = 1.35582 joules. It is the standard unit for bullet, arrow, and projectile energy in the United States.
Use KE = ½mv² with mass in kilograms and velocity in metres per second to get joules, then divide by 1.35582 to convert to foot-pounds. For imperial inputs there is a shortcut: KE (ft·lb) = (grains × fps²) ÷ 450,435. The constant 450,435 bundles all the unit conversions into one number.
A standard 124-grain 9mm Luger leaving the muzzle at 1,150 fps produces about 364 foot-pounds (494 joules) of kinetic energy. +P loads push that to roughly 400–450 ft·lb..45 ACP is similar at around 369 ft·lb, despite being heavier and slower.
A typical hunting arrow weighing 350–400 grains at 280–300 fps carries 60–80 foot-pounds (81–108 J) — well below most handgun cartridges but more than enough for deer at moderate range because arrow lethality depends on cutting tissue, not energy dump.
No. KE = ½mv² works in any consistent unit system. Use kilograms and metres per second to get joules; use slugs and feet per second to get foot-pounds directly without the 450,435 shortcut. Mixing units (pounds with fps, or grams with mph) gives wrong answers — the calculator above handles conversions for you.
Kinetic energy scales with v². A 10% velocity bump yields a 21% energy bump; doubling velocity multiplies energy by four. That is why hunters chase fast loads and why long rifles produce so much more energy than short barrels at the same powder charge.
The unit looks identical but the physical meaning differs. Foot-pound (energy) measures work or kinetic energy. Pound-foot (torque, lbf·ft) measures rotational force. Both are written as ft·lb in everyday use, so context matters — engines produce torque in pound-feet, projectiles carry energy in foot-pounds.
State rules vary, but rule-of-thumb impact-energy minimums are roughly 1,000 ft·lb for deer, 1,500 ft·lb for black bear, and 1,800–2,500 ft·lb for elk, moose, or African plains game. Many jurisdictions also set minimum bullet weight and calibre rules independent of energy.