Percent Error Calculator
Percent error of a measured value against the accepted value, |measured − accepted| ÷ |accepted| × 100, with absolute and relative error and MAPE for a series.
Percent, relative, absolute and signed error, the percent difference with no reference, and for repeated readings the mean, its error, each reading’s error, MAPE and the sample SD.
Example: g measured as 9.60 against 9.81 m/s²: error −0.21, 2.14 % (percent difference 2.16 %); four readings 9.6, 9.7, 9.5, 9.9 average 9.675 — 1.38 % off — with a MAPE of 1.83 %.
Distance from the truth,
as a share of the truth.
What each error figure means, how a series is summarised, and when percent error does not exist.
Percent error
Percent error is |measured − accepted| ÷ |accepted| × 100 — the size of the miss as a share of the accepted (true, theoretical, reference) value. The signed error keeps the direction (positive when you measured high), the absolute error is its size in the original unit, and the relative error is the same share as a fraction. Percent difference, |a − b| ÷ average × 100, is shown alongside for the case where neither value is the reference (two students' readings, two instruments).
A series of readings
Paste repeated readings and the page gives the mean, the percent error of the mean and each reading's own percent error, plus their average (MAPE, mean absolute percent error) and the sample standard deviation. Precision and accuracy are different things: the SD describes the scatter of the readings (precision), the offset of the mean from the accepted value describes accuracy. A small SD with a large offset points to a systematic error — a miscalibrated instrument, a wrong constant.
Edge cases
If the accepted value is zero, percent error is division by zero and is left undefined — report the absolute error, or use percent difference. Tokens in the series that are not numbers are ignored and listed. Nothing is rounded before the calculation; display rounding only. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Percent error = |measured − accepted| ÷ |accepted| × 100; relative error = the same ÷ 100; percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100; MAPE = mean of each reading’s percent error
Last reviewed 22 September 2026. How results are checked: How we verify.