Kinetic energy calculator: find energy, mass or speed

Kinetic energy is the energy an object has because it is moving: KE = ½mv², with mass m in kilograms and speed v in metres per second, giving energy in joules. A 1200 kg car at 20 m/s has ½ × 1200 × 20² = 240,000 J. This kinetic energy calculator finds the energy, or works backwards to the mass or the speed, and also finds the change in kinetic energy when something speeds up or slows down.

It opens on that car. Change the values, or open the full kinetic energy calculator over this page.

Try it

Kinetic Energy Calculator

Find kinetic energy, mass or speed with full working

Open the calculatorGo to its page

How to use the kinetic energy calculator

1. Under Calculate, choose what to find: Energy, Mass, Speed or Change (the change in kinetic energy between two speeds).
2. Type the values you know. Each box has its own unit: mass in g, kg, tonnes or lb, speed in m/s, km/h, mph or km/s, and energy in J, kJ or MJ. The calculator converts them for you.
3. Read the answer, with the steps underneath showing the formula, the numbers going in and the result.
4. Look at the extra results: the momentum, and in Energy mode what the energy would be at twice the speed or with twice the mass.
5. The graph plots kinetic energy against speed, with your speed marked. It curves upwards because energy depends on speed squared.
6. To practise, press Random problem in the Practice section.

The kinetic energy formula

UK courses usually write E_k and US courses KE or K. Square the speed first, then multiply by the mass and halve. The formula is accurate at everyday speeds. Close to the speed of light it no longer applies, and when you type a speed above a tenth of light speed the calculator adds the relativistic value alongside. Rearranged:

Worked examples you can check in the calculator

Example 1: kinetic energy of a car

The car has 240,000 J, or 240 kJ. The calculator also shows that at 40 m/s it would have 960,000 J, four times as much, while a car twice as heavy at 20 m/s would have 480,000 J, only twice as much.

Example 2: converting units first

A 70 kg runner is going at 18 km/h. Convert to m/s by dividing by 3.6: 18 ÷ 3.6 = 5 m/s. Then E_k = ½ × 70 × 5² = 875 J. In the calculator you can leave the speed in km/h and choose km/h as its unit.

Example 3: a ball in grams and miles per hour

A 145 g ball is thrown at 90 mph. In SI units that is 0.145 kg and 90 × 0.44704 = 40.23 m/s:

The ball carries about 117 J. Using 145 instead of 0.145 for the mass would give an answer 1000 times too big, which is why the units matter.

Example 4: finding the speed

A 0.5 kg ball has 100 J of kinetic energy. How fast is it moving? Choose Speed:

It is moving at 20 m/s.

Example 5: finding the mass

An object moving at 10 m/s has 2000 J of kinetic energy. Choose Mass: m = 2 × 2000 ÷ 10² = 4000 ÷ 100 = 40 kg.

Example 6: change in kinetic energy

The 1200 kg car speeds up from 10 m/s to 20 m/s. Choose Change, with initial speed 10 and final speed 20:

Its kinetic energy rises by 180,000 J, from 60,000 J to 240,000 J. Doubling the speed has made it four times bigger. The work-energy principle says the work done on the car equals this change, so the engine (minus losses) did 180 kJ of work. When the final speed is lower, the change is negative and the calculator says the object did work, for example against friction.

Try one

Why speed matters more than mass

Kinetic energy is proportional to mass but to speed squared. Double the mass and the energy doubles. Double the speed and it goes up four times, and three times the speed gives nine times the energy. That is why a car's braking distance grows so quickly with speed: the brakes have to remove all of that kinetic energy as work, so with the same braking force, twice the speed needs about four times the distance.

Common mistakes

• Forgetting to square the speed, or squaring the whole of ½mv instead of just v.
• Forgetting the half. mv² is twice the kinetic energy.
• Wrong units. Use kg and m/s for an answer in joules. Grams and km/h give wrong answers unless you convert or pick the unit in the calculator.
• Squaring the difference in speeds. The change from 10 to 20 m/s uses 20² − 10² = 300, not (20 − 10)² = 100.
• Confusing kinetic energy with momentum. Momentum is mv, in kg m/s, and it has a direction. Kinetic energy is ½mv², in joules, and it doesn't.

Read next

Physics · EnergyKinetic energy equation: Ek = ½mv² explained, with examplesThe kinetic energy equation Ek = ½mv²: what each letter means, how to rearrange it for mass and speed, where it comes from, worked examples and practice.