Kinetic energy calculator with steps

• Energy: a 1,200 kg car moves at 20 m/s. $E_k = 0.5 \times 1200 \times 20^2 = 0.5 \times 1200 \times 400 = 240{,}000$ J (240 kJ).
• Speed: a 2 kg ball has 400 J of kinetic energy. $v = \sqrt{2 \times 400 \div 2} = \sqrt{400} = 20$ m/s.
• Mass: an object moving at 10 m/s has 150 J. $m = 2 \times 150 \div 10^2 = 3$ kg.

Speed is squared, so doubling the speed makes the kinetic energy four times bigger, and tripling it makes it nine times bigger. That's why stopping distances grow so quickly with speed: the brakes have to transfer all of that energy away.

To find speed, rearrange in two steps:

1. Multiply both sides by 2 and divide by $m$: $v^2 = \dfrac{2E_k}{m}$
2. Square root: $v = \sqrt{\dfrac{2E_k}{m}}$

Forgetting the square root is the most common mistake.

When an object falls (ignoring air resistance), the gravitational potential energy it loses becomes kinetic energy: $mgh = \tfrac{1}{2}mv^2$. Use our gravitational potential energy calculator for the other half, and see kinetic energy explained for exam-style questions.

• Squaring the whole $\tfrac{1}{2}mv$ instead of just $v$.
• Using grams instead of kilograms (divide by 1,000).
• Using km/h instead of m/s (divide by 3.6).
• Forgetting the ½.

1. A 0.06 kg tennis ball travels at 30 m/s. What is its kinetic energy?
2. A 900 kg car has 180,000 J of kinetic energy. How fast is it moving?
3. A 2 kg trolley speeds up from 10 m/s to 20 m/s. By how much does its kinetic energy increase?

Answers: 27 J; 20 m/s; from 100 J to 400 J, an increase of 300 J. Check each one with the calculator above.