# Relative Error

## Relative Error

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%.