Kinetic Energy Calculator
The kinetic energy of a moving mass, ½mv², or the mass or speed that gives a kinetic energy, with its momentum.
Result
Kinetic energy: 361,036 ft·lbf
Energy of motion in a straight line at speeds far below that of light.
- Mass
- 3,000 lb
- Speed
- 60 mph (88 ft/s)
- Momentum
- 264,000 lb·ft/s (36,499 kg·m/s)
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How to use the Kinetic Energy Calculator
- Choose whether to find the kinetic energy, the mass or the speed.
- Enter the other two, in whichever units you have. Pounds and miles per hour are converted for you.
- Read the energy in joules or foot-pounds, with the momentum of the same motion.
The formulas
K = ½ × m × v²m = 2K ÷ v²v = √(2K ÷ m)p = m × v, K = p² ÷ 2mThe mass and speed are converted to kilograms and metres per second, so the energy comes out in joules and is then shown in foot-pounds too.
Limits
This is the energy of a body moving as a whole in a straight line. A spinning wheel or a rolling ball has rotational energy on top, and the random motion of the molecules inside, which is heat, is not counted. At speeds approaching that of light the formula underestimates the energy and relativity is needed instead.
With your numbers
- K = ½ × m × v² = ½ × 3,000 lb × (88 ft/s)² = 361,036 ft·lbf
- p = m × v = 264,000 lb·ft/s
Quick reference
Energy of motion in a straight line at speeds far below that of light.
| Example | Result |
|---|---|
| 3,000 lb car at 60 mph | Kinetic energy: 361,036 ft·lbf |
| 1,000 kg car at 100 km/h | Kinetic energy: 385,802 J |
| 80 kg runner at 10 m/s | Kinetic energy: 4,000 J |
| 16 lb bowling ball at 20 mph | Kinetic energy: 213.9 ft·lbf |
| Speed of 80 kg with 4,000 J | Speed: 10 m/s |
| Mass with 4,000 J at 10 m/s | Mass: 80 kg |
Common questions about the Kinetic Energy Calculator
- What is the formula for kinetic energy?
- K = ½mv², half the mass times the speed squared. With the mass in kilograms and the speed in metres per second, the answer is in joules. An 80 kg athlete running at 10 m/s has ½ × 80 × 10² = 4,000 J, the figure in OpenStax University Physics example 7.6.
- Why does doubling the speed quadruple the energy?
- Because the speed is squared. A car at 60 mph carries four times the kinetic energy it has at 30 mph, and all of it has to be taken away by the brakes, or by whatever it hits, to stop it. Doubling the mass only doubles the energy.
- How do I find the speed from the kinetic energy?
- Rearrange to v = √(2K ÷ m). An 80 kg runner with 4,000 J is moving at √(2 × 4,000 ÷ 80) = √100 = 10 m/s. To find a mass instead, use m = 2K ÷ v².
- How are kinetic energy and momentum related?
- Momentum is p = mv, and kinetic energy can be written as K = p² ÷ 2m. The two measure different things: momentum has a direction and is conserved in every collision, while kinetic energy has no direction and is only conserved when nothing is dented, heated or deformed.
- What is a foot-pound?
- The energy of one pound-force acting through one foot, about 1.356 joules. It is the usual imperial unit for the energy of a moving vehicle or a projectile, and the page gives both.