FPE Calculator (Foot-Pounds of Energy)

Related Calculators

FPE: Foot-pounds of energy, written here as ft-lbf. It is a unit of kinetic energy, meaning the energy an object has because it is moving.[2][3]

Kinetic energy: Energy of motion. For a moving mass, it depends on both mass and speed.[2][3]

Grain (gr): A very small mass unit often used for bullets, pellets, and arrows in the US. This calculator converts grains to metric mass before using the physics formula.

fps: Feet per second, a speed unit that tells how many feet the projectile travels each second.

Joule (J): The standard metric unit of energy. This calculator shows energy in both joules and ft-lbf so you can compare either system.[2]

Method agreement check: A comparison between the common grains-plus-fps shortcut and the full kinetic energy conversion method. They should be nearly the same when the inputs are in grains and fps.

Energy delivery factor (percent): An optional user multiplier for rough comparisons. It is not part of the standard definition of kinetic energy.

Mistake: Typing grams into Projectile weight (selected unit) while Weight unit is still set to gr.
Fix: Change Weight unit to g, or enter the value in grains instead. A grams-versus-grains mix-up can change Energy (ft-lbf) by a lot.

Mistake: Entering meters per second in Speed (selected unit) while Speed unit is set to fps.
Fix: Match Speed unit to the number you entered. If your source says m/s, choose m/s so Energy (joules) and Energy (ft-lbf) come out correctly.

Mistake: Using Energy (selected unit) in joules while Energy unit is left on ft-lbf.
Fix: Switch Energy unit to J before calculating in Speed from energy and weight or Weight from energy and speed .

Mistake: Changing Energy delivery factor (percent) below 100 and then treating the reduced result as standard FPE.
Fix: Leave Energy delivery factor (percent) at 100 for normal physics-based kinetic energy. Use other values only for your own comparison scenario.

Mistake: Trying to solve for weight with zero in Speed (selected unit) .
Fix: Enter a speed greater than 0. With zero speed, Weight (grains) and Weight (kilograms) are undefined for this reverse calculation.

Mistake: Seeing an unexpected Method agreement check result and assuming the calculator is wrong.
Fix: First confirm you are in Energy (FPE) from weight and speed mode with Weight unit set to gr and Speed unit set to fps. Outside that setup, the shortcut comparison is not applicable.

• This calculator treats FPE as kinetic energy of a moving object only. It does not estimate recoil, penetration, stopping power, or any real-world effect by itself.
• The shortcut formula applies only when Projectile weight (selected unit) is in grains and Speed (selected unit) is in fps. In other unit combinations, the calculator uses unit conversions and the main physics formula.
• Energy delivery factor (percent) is optional and user-defined. Changing it creates a comparison value, not a new physics law.
• Solving for weight requires speed greater than 0. If speed is 0, the reverse weight calculation is undefined.
• Solving for speed allows energy equal to 0, which gives speed 0 as long as the projectile weight is greater than 0.
• Results can differ slightly from hand calculations because of rounding and display format choices such as fixed decimals or scientific notation.
• Presets are only quick starting points. Always verify the actual projectile weight from your own source before using the result.

What the calculator does

This calculator uses the standard kinetic energy idea: moving mass has energy because of its motion.[2][3] It can solve for energy, speed, or projectile weight, then convert the result into the other common units shown on the page.

Main formulas

E_J = 0.5 * m_kg * v_mps^2

E_ftlbf = E_J / 1.3558179483314004

E_ftlbf = (w_gr * v_fps^2) / 450240

v_mps = sqrt((2 * E_J) / m_kg)

m_kg = (2 * E_J) / v_mps^2

E_delivered = E * (delivery_factor_percent / 100)

How units are handled

The calculator first converts the entered mass to kilograms and speed to meters per second, then applies the kinetic energy formula.[3] After that, it converts energy to ft-lbf when needed. If you enter grains and fps while solving for energy, it also computes the common shortcut formula and compares both methods.

The shortcut denominator 450240 is just the regular kinetic energy formula with grain-to-mass, foot-to-meter, and joule-to-ft-lbf conversions built in. That is why the shortcut should closely match the full physics method when the units are exactly grains and fps.

Worked mini-example

Suppose Projectile weight (selected unit) is 150 gr and Speed (selected unit) is 2800 fps.

Convert 150 gr to kilograms:

150 x 0.00006479891 = 0.0097198365 kg.

Convert 2800 fps to meters per second:

2800 x 0.3048 = 853.44 m/s.

Then apply kinetic energy.[3]

E_J = 0.5 * 0.0097198365 * 853.44^2 = about 3541.91 J

E_ftlbf = 3541.91 / 1.3558179483314004 = about 2612.24 ft-lbf

Using the shortcut gives nearly the same result:

E_ftlbf = (150 * 2800^2) / 450240 = about 2612.24 ft-lbf

If your agreement result is not close, the most likely cause is a unit mix-up.

Reverse solving

For Speed from energy and weight, the calculator converts the entered energy to joules and the entered projectile weight to kilograms, then solves for speed from the kinetic energy formula. If energy is 0 and weight is positive, speed is 0.

For Weight from energy and speed, it converts energy and speed to SI units first, then solves for mass. If speed is 0, the result is undefined because the formula would divide by zero.

Assumptions used

This tool assumes the projectile is treated as a point mass and that you want ideal kinetic energy only.[2][3] It does not model drag, shape, tumbling, deformation, launch system losses, or target behavior. The optional delivery factor is only an extra user multiplier for rough comparisons, not part of the physics definition.