Percent Error Calculator

The formula and what goes where

Percent error is |measured - accepted| / |accepted| × 100. The accepted value belongs in the denominator, and that is not arbitrary — the whole point is to express the error as a proportion of the thing you were trying to measure. Dividing by the measured value instead gives a different number, and for large errors a noticeably different one. Whether to take the absolute value is a matter of convention: introductory courses usually want a positive figure, while error analysis often keeps the sign so that a systematic bias in one direction stays visible across repeated measurements.

Error, difference, and uncertainty

Three related ideas get confused constantly. Percent error needs a known correct value to compare against. Percent difference compares two measurements when neither is privileged, and divides by their mean rather than by either one — which is why it is symmetric and percent error is not. Uncertainty is different again: it is the range within which the true value plausibly lies, derived from the precision of the instrument and the spread of repeated readings, and it exists even when no accepted value is available.

Accurate is not the same as precise

Accuracy is closeness to the true value; precision is repeatability. A balance that reads 7.3421 g every single time for a 5.0000 g standard is extremely precise and badly inaccurate, almost certainly because of a calibration offset. The opposite also happens: readings scattered widely around the right answer average out well but no single reading can be trusted. Percent error measures accuracy only, so a small percent error from one reading says nothing about whether the next reading will agree.

When the accepted value is zero

The formula breaks down. Dividing by zero is undefined, and there is no sensible way to express an absolute error as a proportion of nothing — an error of 0.01 against a true value of 0 is infinitely wrong in percentage terms, which is mathematically correct and practically useless. This calculator refuses that case and says why rather than printing an infinity symbol or, worse, silently substituting some small number. Where the expected value legitimately is zero, report the absolute error and the instrument's uncertainty instead.

What counts as an acceptable error

It depends entirely on the field. A school titration within 5% is usually fine; an analytical laboratory would regard that as a failed run. Structural engineering works to fractions of a percent on material properties, while a first estimate in astrophysics being within a factor of two is often considered a good result. Quoting a percent error without saying what the acceptable threshold is leaves out the half of the statement that carries the meaning.

Frequently Asked Questions