Kinetic Energy Calculator
Find an object's kinetic energy from its mass and speed, or turn the formula around to find the mass or the speed from the energy. A second mode handles spinning objects, ½Iω². Pick any units — km/h, mph, rpm, pounds, kilojoules — and get the answer with the working, the same energy in joules, kWh, kcal, ft·lbf and more, and what happens to it if the speed changes. Runs in your browser; free, no sign-up.
Kinetic energy is the energy of motion. Enter the object's speed, not its velocity vector — the direction does not matter because the speed is squared.
Calculated
Results
200000 J
Kinetic energy KE
The working
- Start from KE = ½ × m × v².
- Convert to SI units: v = 72 km/h = 20 m/s.
- KE = ½ × 1000 × 20² = 200000 J
The same energy in other units
| Unit | Energy |
|---|---|
| J | 200000 |
| kJ | 200 |
| kcal | 47.8 |
| Wh | 55.56 |
| kWh | 0.05556 |
| ft·lbf | 147500 |
| Btu | 189.6 |
| eV | 1.248 × 10²⁴ |
What if the speed changed?
| Speed | Kinetic energy | Compared with now |
|---|---|---|
| 0.5 × the speed | 50000 J | 0.25 × |
| 2 × the speed | 800000 J | 4 × |
| 3 × the speed | 1.8 × 10⁶ J | 9 × |
Uses the classical (non-relativistic) formulas, which are accurate for everyday speeds. Kinetic energy is a scalar, so it is never negative and has no direction.
How to Use the Kinetic Energy Calculator
- 1. Choose what is moving. An object moving along uses KE = ½mv². A spinning object uses KE = ½Iω².
- 2. Pick the unknown. Select kinetic energy, mass (or moment of inertia) or speed (or angular speed). The box you are solving for becomes the answer, and your other entries stay put when you switch.
- 3. Enter the rest with units. Each box has a unit menu. Scientific notation such as 9.1e-31 works for very small or large values.
- 4. Read the working and the extras. You get the substitution, the energy in other units, and a table showing how the energy changes with speed.
The Formulas
| Motion | Formula | Units |
|---|---|---|
| Moving along | KE = ½ m v² | kg and m/s give joules (1 J = 1 kg·m²/s²) |
| Spinning | KE = ½ I ω² | I in kg·m², ω in rad/s |
| Mass from energy | m = 2 KE ÷ v² | Needs a speed above zero |
| Speed from energy | v = √(2 KE ÷ m) | Gives the speed, never negative |
Reference: OpenStax University Physics, Volume 1, sections 7.2 and 10.4. The calculator converts rpm to rad/s by multiplying by 2π ÷ 60.
The speed is squared, so kinetic energy grows much faster than speed does: double the speed and the energy quadruples; triple it and the energy is nine times as large. That is why a crash at 100 km/h is far worse than one at 50 km/h, and why braking distance grows with the square of speed.
Worked Examples
A car. A 1,000 kg car travels at 72 km/h, which is 20 m/s. KE = ½ × 1000 × 20² = 200,000 J, or 200 kJ (the calculator's default). That is 0.05556 kWh, 47.8 kcal or about 147,500 ft·lbf. At half the speed it would carry 50,000 J; at twice the speed, 800,000 J; at three times, 1.8 MJ.
A flywheel. A flywheel with I = 0.5 kg·m² spins at 3,000 rpm. Converting, ω = 3000 × 2π ÷ 60 = 314.2 rad/s, so KE = ½ × 0.5 × 314.2² = 24,670 J — about 24.7 kJ stored in the rotation.
| Object | Mass | Speed | Kinetic energy |
|---|---|---|---|
| Baseball pitch | 0.145 kg | 40 m/s | 116 J |
| Sprinter | 70 kg | 10 m/s | 3,500 J |
| Rifle bullet | 0.004 kg | 900 m/s | 1,620 J |
| Car | 1,000 kg | 20 m/s | 200,000 J |
Kinetic Energy and Work
The work–energy theorem says the net work done on an object equals its change in kinetic energy. To stop the 1,000 kg car above, the brakes must remove 200 kJ; with a constant braking force of 5,000 N that takes 40 m. For energy stored by position rather than motion, see the Potential Energy Calculator.
Limits of the Formula
½mv² is the classical formula. At everyday speeds it is excellent. The relativistic kinetic energy is (γ − 1)mc², and ½mv² falls more than 1% short of it once v passes about 11.5% of the speed of light (roughly 34,000 km/s). The calculator warns you when you go beyond that.
Frequently Asked Questions
- What is the formula for kinetic energy?
- KE = ½ m v², where m is the mass in kilograms and v is the speed in metres per second, giving joules. For a spinning object use KE = ½ I ω², with the moment of inertia I and the angular speed ω in radians per second.
- Why is kinetic energy proportional to speed squared?
- Because the work needed to reach a speed is force times distance, and with constant acceleration the distance covered also grows with speed squared (v² = 2as). The two effects combine so energy depends on v², not v.
- Can kinetic energy be negative?
- No. Mass is positive and the speed is squared, so kinetic energy is zero or positive, whatever the direction of motion. A negative velocity gives the same energy as a positive one.
- What is the difference between kinetic energy and momentum?
- Momentum, p = mv, is a vector that depends on speed linearly and is conserved in every collision. Kinetic energy is a scalar that depends on speed squared and is only conserved in elastic collisions. The two are linked by KE = p² ÷ 2m.
- How do I convert joules to kilowatt-hours?
- Divide by 3,600,000, because 1 kWh = 3.6 × 10⁶ J. So 200,000 J is 0.05556 kWh. The calculator lists the result in kWh, kcal, ft·lbf, Btu and eV beside joules.
- How much kinetic energy does a spinning object have?
- It depends on how the mass is spread out. A solid disk has I = ½MR², a hoop MR², so a hoop of the same mass and radius stores twice the energy at the same spin rate. The torque calculator gives I for common shapes.