relative error

The absolute error measured as a fraction of the exact value's own size, so a gap of 1 can be tiny or huge depending on the context.

The relative error of an approximation $\tilde{x}$ to a nonzero exact value $x$ is $\dfrac{|x-\tilde{x}|}{|x|}$ -- the absolute error scaled by how large $x$ itself is, undefined when $x=0$ .

Examples

An absolute error of 1 is enormous for $x=2$ (relative error 0.5) but negligible for $x=10{,}000{,}000$ (relative error $10^{-7}$ ).