Absolute value of the ratio \(\dfrac{ε}{x}\) between the absolute error ε and the exact value

*x*.\(\left | \dfrac{ε}{x} \right | = \left | \dfrac{α\space−\space{x}}{x} \right | \)

The relative error is often expressed as a percentage.

### Example

If the absolute error of a measure is ε = 0.2 m on a measure of 40 m, then the relative error is given by: \(\dfrac{40.2 − 40}{40} = 0.005\). Therefore, the relative error is 0.5%.