Definition:Error/Relative

Definition

Let $x_0$ be an approximation to a (true) value $x$.

The relative error of $x_0$ in $x$ is defined as:

$\delta x := \dfrac {\Delta x} x$

where $\Delta x$ denotes the absolute error of $x_0$.

This can be defined only when $x \ne 0$.

Also defined as

The relative error of $x_0$ in $x$ can also be defined as:

$\delta x \approx \dfrac {\Delta x} {x_0}$

where:

$\Delta x$ denotes the absolute error of $x_0$

$\approx$ indicates that the value is but approximate.

This can be particularly useful when the true value $x$ can only be speculated.

Also see

• Definition:Absolute Error
• Definition:Percentage Error

• Results about errors can be found here.

Sources

• 1964: Milton Abramowitz and Irene A. Stegun: Handbook of Mathematical Functions ... (previous) ... (next): $3$: Elementary Analytic Methods: $3.5$ Absolute and Relative Errors: $3.5.2$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): error: 1.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): relative error
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): relative error
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): relative error