How to Calculate Kinetic Energy

To calculate kinetic energy, multiply an object's mass by its speed squared, then divide by two:

$$E_k=\frac{1}{2}m{v}^2$$

Here, $E_k$ is kinetic energy in joules ($\mathrm{J}$), $m$ is mass in kilograms ($\mathrm{kg}$), and $v$ is speed in metres per second ($m/s$). Kinetic energy is energy stored by a moving object. This calculation is part of AQA GCSE Physics at both Foundation and Higher tier.

Worked example

Suppose an object has a mass of $2\mathrm{kg}$ and moves at $3m/s$. First square the speed: $3^2=9$. Then substitute into the equation:

$$E_k=\frac{1}{2}\times 2\times 3^2=\frac{1}{2}\times 2\times 9=9\mathrm{J}$$

So the object has $9\mathrm{J}$ of kinetic energy. Writing the substitution step makes it easier to check that each value is in the right place. Notice that you square the number representing speed before multiplying it by the mass; you do not square the entire calculation.

Check the units

The equation uses kilograms and metres per second. If the question gives a mass in grams, convert it to kilograms before substituting. For example, $500\mathrm{g}=0.5\mathrm{kg}$. Use the converted value in the calculation, and give the resulting kinetic energy in joules. If the speed is given in kilometres per hour, convert it to metres per second first as well. Keeping the units alongside your numbers helps you spot a conversion you might otherwise miss.

Common mistake

Square the speed, not the mass. Calculating ${\left(\frac{1}{2}mv\right)}^2$ squares the whole expression and will usually give the wrong answer. Check that your working follows $\frac{1}{2}\times m\times v^2$.

The squared speed also explains how kinetic energy changes. If the mass stays the same but the speed doubles, kinetic energy becomes four times as large, because $(2v{)}^2=4v^2$. Doubling the mass instead would double the kinetic energy, provided the speed stayed the same.