Kinetic Energy Calculator
Calculate kinetic energy (½mv²) or gravitational potential energy (mgh) and solve for any missing variable, with mass, speed, height and energy in the units you use. Everything runs privately in your browser.
KE = ½ m v²
PE = m g h
How to use the Kinetic Energy Calculator
- Choose a tab: Kinetic energy for moving objects or Potential energy for height above the ground.
- Pick what to solve for with the Solve for buttons, e.g. Energy, Mass, Velocity or Height.
- Enter the known values and choose a unit next to each one (kg or lb, km/h or mph, m or ft).
- Read the answer in the highlighted field and the result card; change its unit to convert it instantly.
- Check the working in the step-by-step solution, then press Copy result to paste it into your notes.
Kinetic and potential energy formulas
Kinetic energy is the energy an object has because it is moving: KE = ½mv². With mass in kilograms and speed in metres per second, the answer is in joules (1 J = 1 kg·m²/s²). Rearranged, the same formula gives the mass m = 2KE / v² or the speed v = √(2KE / m).
Gravitational potential energy is the energy stored by lifting an object: PE = mgh, with g the gravitational acceleration (standard Earth gravity is 9.80665 m/s²) and h the height above your reference level. If the object then falls freely, that energy turns into kinetic energy, so the impact speed is v = √(2gh) whatever the mass.
Worked examples
| Object | Mass | Speed or height | Energy |
|---|---|---|---|
| Car on a highway | 1,500 kg | 100 km/h (27.78 m/s) | ≈ 578.7 kJ |
| Fastball | 145 g | 95 mph (42.47 m/s) | ≈ 130.8 J |
| Rifle bullet | 8 g | 900 m/s | 3,240 J |
| Sprinter | 80 kg | 10 m/s | 4,000 J |
| Book on a shelf | 1 kg | 2 m high (Earth) | ≈ 19.6 J |
| Water in a dam | 1,000 kg | 100 m high (Earth) | ≈ 980.7 kJ (0.272 kWh) |
Notice how the car at 100 km/h carries about the same energy as a tonne of water dropped 60 metres. Because speed is squared, a car at 130 km/h has 69% more kinetic energy than at 100 km/h, which is why stopping distances grow so quickly with speed.
Energy unit conversions
| Unit | In joules |
|---|---|
| 1 kilojoule (kJ) | 1,000 J |
| 1 calorie (thermochemical, cal) | 4.184 J |
| 1 kilocalorie (kcal, food Calorie) | 4,184 J |
| 1 watt-hour (Wh) | 3,600 J |
| 1 kilowatt-hour (kWh) | 3,600,000 J |
| 1 foot-pound force (ft·lbf) | 1.355818 J |
| 1 BTU (International Table) | 1,055.056 J |
| 1 electronvolt (eV) | 1.602176634 × 10⁻¹⁹ J |
Gravity presets use NASA planetary fact sheet surface values, e.g. Moon 1.62 m/s², Mars 3.71 m/s² and Jupiter 24.79 m/s². To see how speed relates to distance and time, try the speed distance time calculator; for engines, the horsepower calculator converts torque and rpm to power.
Frequently asked questions
What is the formula for kinetic energy?
Kinetic energy is KE = ½mv², where m is the mass in kilograms and v is the speed in metres per second. The result is in joules (J). For example, a 1,500 kg car at 100 km/h (27.78 m/s) has ½ × 1500 × 27.78² ≈ 578,700 J, or about 579 kJ.
Why does doubling the speed quadruple the kinetic energy?
Because speed is squared in ½mv². Going from 50 to 100 km/h multiplies v² by 4, so the car carries four times the energy and needs roughly four times the braking distance. Doubling the mass only doubles the energy.
How do I find velocity from kinetic energy?
Rearrange the formula to v = √(2·KE / m). Select Velocity under Solve for, enter the energy and mass, and the calculator converts the units and gives the speed in m/s, km/h, mph, ft/s or knots.
What is the potential energy formula?
Gravitational potential energy near a planet's surface is PE = mgh: mass (kg) × gravitational acceleration (m/s²) × height (m). On Earth standard gravity is g = 9.80665 m/s², so lifting 2 kg by 10 m stores about 196 J.
How are kinetic and potential energy related?
Without air resistance, an object that falls from height h converts all its potential energy into kinetic energy, so mgh = ½mv² and the impact speed is v = √(2gh), independent of mass. The Potential energy tab shows this impact speed as an extra.
Which units can I use?
Mass in kg, g, mg, tonnes, pounds and ounces; speed in m/s, km/h, mph, ft/s, knots and km/s; height in m, cm, mm, km, in, ft, yd and miles; energy in joules, kJ, MJ, calories, kilocalories, Wh, kWh, foot-pounds, BTU and electronvolts.
Is the calculator accurate for very fast objects?
½mv² is the classical formula and is accurate for everyday speeds. Near the speed of light (above about 10% of c) you need the relativistic formula KE = (γ − 1)mc², which gives larger values.