Relative Error

Relative error is the absolute error divided by the magnitude of the exact value.

$$E_{\text{rel}}=\frac{|y_{\text{approx}}-y_{\text{exact}}|}{|y_{\text{exact}}|}$$

Relative error is dimensionless and scale-independent, making it more meaningful than Absolute error when comparing errors across quantities of very different sizes. It expresses the error as a fraction of the true value.

Absolute error | Order of a method | Order of convergence