How to Calculate Kinetic Energy from Mass and Speed

Calculates kinetic energy as E = ½ × mass × speed². Mass is in kilograms, speed in m/s, and energy in joules.

Explanation

Kinetic energy is the energy an object has because it is moving. Its mass and its speed are all you need.

E = \dfrac{1}{2} m v^2

$E$ is the kinetic energy, in joules (J)
$m$ is the mass, in kilograms (kg)
$v$ is the speed, in metres per second (m/s)

The thing to remember is that the speed is squared. Doubling the mass doubles the energy, but doubling the speed multiplies the energy by four, and tripling it by nine. That is why stopping distances grow so sharply as a car goes faster.

Example

The defaults are a mass of 2 kg and a speed of 3 m/s.

E = \dfrac{1}{2} \times 2 \times 3^2 = 9\,\mathrm{J}

The kinetic energy is 9 J. Bringing the object to rest takes 9 J of work, done by a brake or by friction.

Notes

Only the size of the speed matters, not its direction. Moving at 3 m/s to the left and at 3 m/s to the right both give 9 J. Kinetic energy is never negative, and it is zero for an object at rest.

Use kilograms and metres per second. A speed given in km/h has to be divided by 3.6 first: 72 km/h is 20 m/s.

This is the everyday formula, valid for objects moving far more slowly than light.

A spinning object stores rotational energy on top of this. What you get here is the energy of travelling from place to place.