FPE Calculator - Foot-pounds of Energy
Turn a weight in grains and a speed in feet per second into foot-pounds and joules, check the 450240 shortcut, and convert energy between units.
👣 What is FPE (Foot-pounds of Energy)?
FPE stands for foot-pounds of energy, the amount of kinetic energy a moving object carries when that energy is written in the US customary unit foot-pound-force (ft-lbf). One foot-pound is the work done when a force of one pound-force moves an object through one foot, which is exactly 1.3558179483314004 joules. FPE is not a different kind of energy. It is the same kinetic energy KE = ½ m v² that a physics class measures in joules, simply expressed in a unit that is still common in the United States for air guns, archery, tools and engineering handbooks.
The reason FPE calculators ask for weight in grains and speed in feet per second is practical. Small projectiles and pellets are sold by grain weight, and speed is quoted in fps, so a shortcut formula was built to take those two numbers directly: FPE = grains × fps² ÷ 450,240. This calculator gives you that shortcut, but its main result comes from the exact SI route: convert the weight to kilograms, the speed to metres per second, compute joules, and divide by 1.3558179483. You then see both numbers and the percent difference, which is about 0.044 percent, so you know how much the rounding in the constant matters.
Typical uses are neutral and educational. Students convert a thrown baseball or a swinging hammer into foot-pounds to compare it with a textbook that uses joules. Archers and hobbyists compare the kinetic energy of an arrow in ft-lbf against joules on a spec sheet, and the arrow speed calculator estimates how fast a given bow launches it. Makers working with spring launchers, airsoft BBs or low-energy air-gun pellets use the same arithmetic at illustrative low energies. Because the formula is plain classical mechanics, it also works for a pendulum bob or any rolling cart.
Three cautions keep results meaningful. First, the energy is quadratic in speed: doubling the speed multiplies the energy by four, while doubling the weight only doubles it, which the chart shows with half-weight and double-weight curves. Second, foot-pounds of energy and foot-pounds of torque share a name but measure different things. Third, a single energy number does not describe everything about a moving object, since momentum, shape and how energy is transferred also matter. The calculator therefore also reports momentum in lb-ft/s and kg m/s. For deeper background, see the kinetic energy calculator, the muzzle velocity calculator and the momentum calculator.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - A 100 grain object at 300 fps
A 100 grain test mass moving at 300 feet per second
Example 2 - Convert 1 foot-pound to other units
One foot-pound of energy written in every unit
Example 3 - A 450 grain arrow at 250 fps
An archery arrow weighing 450 grains moving at 250 fps
Example 4 - A thrown baseball
A 145 g baseball thrown at 40 m/s
Example 5 - Speed from energy and weight
How fast must a 100 grain object move to carry 20 ft-lbf?
❓ Frequently Asked Questions
🔗 Related Calculators
How do you calculate foot-pounds of energy from grains and fps?
Multiply the weight in grains by the velocity in feet per second squared, then divide by 450,240. A 100 grain object at 300 fps gives 100 x 300^2 / 450,240 = 19.99 ft-lbf. The exact SI route gives 19.98 ft-lbf.
Where does the 450,240 constant come from?
It folds three things together: the factor of 2 in KE = 1/2 m v^2, 7,000 grains per pound, and gravity. 450,240 equals 2 x 7,000 x 32.16. With the standard 32.17405 ft/s^2 the constant would be about 450,437.
How many joules is one foot-pound of energy?
One foot-pound-force of energy is exactly 1.3558179483314004 joules. So 1 J is 0.7376 ft-lbf, and 100 ft-lbf is 135.58 J.
How do I convert ft-lbf to joules?
Multiply foot-pounds by 1.3558179483314004. For example 20 ft-lbf x 1.3558 = 27.12 J. To go the other way, divide joules by 1.3558, or multiply by 0.7376.
How many grains are in a pound and a gram?
There are exactly 7,000 grains in an avoirdupois pound, and one grain is exactly 64.79891 mg. So 1 g is about 15.43 grains and 100 grains is 6.48 g.
Why does doubling speed quadruple the energy?
Kinetic energy is 1/2 m v^2, so it grows with the square of speed. A 100 grain object at 300 fps carries 19.98 ft-lbf, and at 600 fps it carries 79.92 ft-lbf, which is four times as much.
How many foot-pounds are in a joule, calorie or BTU?
1 J is 0.7376 ft-lbf, 1 thermochemical calorie (4.184 J) is 3.086 ft-lbf, 1 kilocalorie is 3,085.96 ft-lbf, and 1 International Table BTU (1,055.056 J) is 778.17 ft-lbf.
Is foot-pound of energy the same as foot-pound of torque?
No. Both use the name foot-pound, but energy is force times distance along the force, while torque is force times a lever arm at right angles. The units are dimensionally the same, yet they measure different things.
How do I find speed from energy and weight?
Use v = sqrt(2E / m) in SI units, or the shortcut v = sqrt(450,240 x FPE / grains). A 100 grain object carrying 20 ft-lbf moves at about 300.1 ft/s. The speed mode does this for you.
What is the difference between pounds, slugs and lbm in the energy formula?
Weight in pounds is a force, and mass in slugs is pounds divided by 32.174. Writing the grain formula as 1/2 x (grains/7000) x v^2 / 32.174 gives foot-pounds directly, which is exactly where the 450,000 style constant comes from.
Does the same formula work for a baseball or a hammer swing?
Yes. Kinetic energy is KE = 1/2 m v^2 for any object. A 145 g baseball at 40 m/s carries 116 J, which is 85.56 ft-lbf. Only the units are chosen to match grains and fps.