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Relative Error

Let the true value of a quantity be $x$ and the measured or inferred value $x_0$. Then the relative error is defined by

\delta x={\Delta x\over x}={x_0-x\over x}={x_0\over x}-1,

where $\Delta x$ is the Absolute Error. The relative error of the Quotient or Product of a number of quantities is less than or equal to the Sum of their relative errors. The Percentage Error is 100% times the relative error.

See also Absolute Error, Error Propagation, Percentage Error


Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 14, 1972.

© 1996-9 Eric W. Weisstein