Math & Science
Kinetic Energy Calculator
Work out the energy of a moving object — or rearrange it to find the mass or speed instead.
Kinetic Energy Calculator
About the Kinetic Energy Calculator
Kinetic energy is the energy an object carries because it is moving. The formula is one half times mass times velocity squared, and this calculator solves it in whichever direction you need — energy from mass and speed, or mass or speed from a known energy.
Results come in joules, kilojoules and calories, with the object's momentum shown alongside. Momentum and kinetic energy are easy to confuse, and seeing both together makes the difference obvious.
Use SI units for a clean answer: mass in kilograms, velocity in metres per second, energy in joules. The page below explains what goes wrong if you mix in grams or km/h without converting.
How to use the Kinetic Energy Calculator
- Choose which variable to solve for. That field disappears.
- Enter the two values you know.
- Use SI units: kilograms and metres per second.
- Select Calculate.
- Momentum is shown alongside since it is often wanted at the same time.
Kinetic energy formula (equation), three ways
KE = ½ m v²
m = 2 × KE ÷ v²
v = √(2 × KE ÷ m)
m in kilograms, v in metres per second, KE in joules.
Worked example
A 1,200 kg car travelling at 25 m/s (90 km/h).
KE = ½ × 1200 × 25² = 0.5 × 1200 × 625
375,000 joules — 375 kJ
Momentum is m × v = 30,000 kg·m/s. Now double the speed to 50 m/s: momentum doubles to 60,000, but kinetic energy quadruples to 1,500 kJ. That gap is the whole reason speed matters so much in a crash.
Why doubling speed quadruples the energy
Because velocity is squared in the formula while mass is not. Double the mass and the energy doubles. Double the speed and it goes up four times, since 2² = 4.
| Speed | Multiple of 25 m/s | Energy (1,200 kg car) | Multiple |
|---|---|---|---|
| 12.5 m/s | ½× | 93.75 kJ | 0.25× |
| 25 m/s | 1× | 375 kJ | 1× |
| 37.5 m/s | 1.5× | 844 kJ | 2.25× |
| 50 m/s | 2× | 1,500 kJ | 4× |
| 75 m/s | 3× | 3,375 kJ | 9× |
This is why a 20% speed increase raises crash energy by 44%, and why braking distance grows with the square of speed rather than in proportion to it. The energy has to go somewhere, and in a collision it goes into deforming metal and people.
Kinetic energy and momentum are different quantities
| Kinetic energy | Momentum | |
|---|---|---|
| Formula | ½mv² | mv |
| Type | Scalar — no direction | Vector — has direction |
| Unit | Joule (J) | kg·m/s |
| Doubling speed | ×4 | ×2 |
| Conserved in a collision | Only if perfectly elastic | Always |
Momentum is always conserved in a collision. Kinetic energy usually is not — some converts to heat, sound and permanent deformation. A collision that conserves both is called elastic, and outside of billiard balls and gas molecules, few real ones come close.
Units, and what happens if you mix them
- Mass in kilograms, not grams. Using grams makes the answer 1,000 times too large.
- Velocity in metres per second, not km/h. Using km/h inflates the result by roughly 13 times, because the error is squared.
- Energy in joules. One joule is one kg·m²/s².
- Calories shown here are thermochemical calories, at 4,184 J per food Calorie (kcal).
Some energies for scale
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Tennis ball, served | 58 g | 55 m/s | 88 J |
| Cricket ball, fast bowl | 160 g | 40 m/s | 128 J |
| Sprinting adult | 70 kg | 10 m/s | 3,500 J |
| Car at 50 km/h | 1,200 kg | 13.9 m/s | 116 kJ |
| Car at 100 km/h | 1,200 kg | 27.8 m/s | 464 kJ |
| Loaded lorry at 90 km/h | 40,000 kg | 25 m/s | 12,500 kJ |
For working out the speed itself, use the velocity calculator. For how quickly that speed changed, try the acceleration calculator.
Rotational kinetic energy formula
Spinning objects store energy too. For rotation, mass becomes moment of inertia (I) and speed becomes angular velocity (ω):
KErot = ½ × I × ω²
A flywheel with I = 2 kg·m² spinning at 50 rad/s holds ½ × 2 × 2,500 = 2,500 J. A rolling wheel has both kinds: add the straight-line KE and the rotational KE.
Arrow kinetic energy calculator (archery)
Bowhunters use feet and grains, so there is a special version of the formula:
KE (ft·lb) = arrow weight (grains) × speed (ft/s)² ÷ 450,240
A 400-grain arrow at 280 ft/s: 400 × 78,400 ÷ 450,240 = 69.7 ft·lb. A common guideline is about 25 ft·lb for small game, 41–65 for deer, and 65 or more for elk. Check your local hunting rules.
Units of kinetic energy: joules and foot-pounds
The SI unit is the joule (J). One joule is the energy of a 2 kg mass moving at 1 m/s. Other units you may meet:
- 1 foot-pound (ft·lb) = 1.356 J
- 1 kilocalorie (food Calorie) = 4,184 J
- 1 kilowatt-hour = 3,600,000 J
What is kinetic energy?
Kinetic energy is the energy an object has because it is moving. Anything with mass and speed has it: a rolling ball, a flowing river, a speeding car. Stop the object and that energy has to go somewhere — into heat in the brakes, sound, or bent metal.
How to calculate kinetic energy
To calculate kinetic energy, use the equation for kinetic energy, KE = ½mv², with mass in kilograms and speed in metres per second. A 1,500 kg car at 25 m/s (about 56 mph) has ½ × 1,500 × 25² = 468,750 J, or about 345,750 foot-pounds.
Change in kinetic energy, and kinetic plus potential energy
Change in kinetic energy: ΔKE = ½m(v² − u²)
Potential energy: PE = mgh
Mechanical energy = KE + PE
The change in kinetic energy equals the work done on the object. Drop a 2 kg ball from 5 m and its potential energy, 2 × 9.81 × 5 = 98 J, turns into about 98 J of kinetic energy just before it lands, ignoring air resistance.
For bullets and arrows, a foot-pounds of energy calculator uses grains and feet per second: ft-lb = weight (grains) × velocity² ÷ 450,240. A 124-grain bullet at 1,150 fps carries about 364 ft-lb.
Other ways to use this calculator
KE = ½mv² covers many fields.
- Arrow kinetic energy calculator — use the archery formula above with grains and feet per second.
- Bullet kinetic energy calculator — convert grains to kilograms (÷ 15,432) and ft/s to m/s (× 0.3048), or use foot-pounds directly.
- Kinetic energy solver — solve for energy, mass or velocity.
- KE formula — kinetic energy is half m v squared: half mv squared, with mass in kg and speed in m/s.
- Joules calculator — results are in joules, the SI unit of energy.
Frequently asked questions
Kinetic energy is KE = ½mv² — half the mass times the velocity squared. A 1,200 kg car at 25 m/s carries 0.5 × 1200 × 625 = 375,000 joules, or 375 kJ. Use kilograms for mass and metres per second for velocity to get joules. Rearranged, the formula also gives mass as 2KE ÷ v² and velocity as √(2KE ÷ m).
Because velocity is squared in the formula and mass is not. Doubling the mass doubles the energy, but doubling the speed multiplies it by 2² = 4. Tripling speed multiplies energy by nine. This is why crash severity rises so steeply with speed, and why stopping distance grows with the square of speed rather than in proportion to it.
Kilograms for mass, metres per second for velocity, and the answer comes out in joules. Mixing units causes large errors because of the squaring: using grams makes the result 1,000 times too big, and using km/h instead of m/s inflates it by about 13 times. Convert everything to SI before you calculate, not afterwards.
Kinetic energy is ½mv², a scalar measured in joules. Momentum is mv, a vector measured in kg·m/s. Doubling speed doubles momentum but quadruples energy. Momentum is always conserved in a collision; kinetic energy is conserved only in a perfectly elastic one, since real impacts convert some energy into heat, sound and deformation.
The joule (J), equal to one kilogram metre squared per second squared. Use mass in kilograms and speed in metres per second to get joules. In archery and ballistics, foot-pounds are also common (1 ft·lb = 1.356 J).
KE = ½mv², where m is mass in kilograms and v is speed in metres per second. The answer is in joules. Doubling the speed makes the kinetic energy four times larger.
Sources and further reading
- NIST — Guide for the Use of the International System of Units — the joule and SI units for energy and momentum
- NIST — Fundamental physical constants — unit definitions used in the conversions
- Kinetic energy — Encyclopaedia Britannica — the derivation and the energy/momentum distinction