Percent Error Calculator

How far an experimental or measured value is from the theoretical/accepted value, as a percentage

Percent error quantifies how far an experimental or measured value deviates from a theoretical or accepted reference value, expressed as a percentage of that reference value — a standard way to communicate measurement accuracy that's independent of the absolute units or magnitude of what's being measured.

Why percent error is expressed relative to the accepted value, not the measured one

Percent error is calculated as the absolute difference between measured and accepted values, divided by the accepted (theoretical/reference) value — not the measured value — then expressed as a percentage. This specific choice of denominator matters: dividing by the accepted value gives a consistent, standard measure of accuracy relative to what the "true" or expected value actually is, which is the conventional and meaningful framing for most measurement-accuracy contexts (a lab experiment's result compared against a known theoretical value, for instance). Using the measured value as the denominator instead would give a different number and represents a different (less standard) framing of the same underlying deviation.

A worked example

The same absolute deviation between a measured and accepted value produces different percent error figures depending on the magnitude of the accepted value itself — an identical absolute error represents a much larger percent error against a small accepted value than against a large one, which is exactly why percent error (a relative measure) is more informative for comparing accuracy across different-scale measurements than absolute error alone would be.

How this connects to your other math and science calculations

Percent error is one of several ways to express deviation or uncertainty in a measurement — for the related but distinct question of how much confidence a sample-based estimate carries (rather than how far a single measurement deviates from a known reference), the Confidence Interval Calculator covers that separate statistical concept.

Common mistakes

Dividing by the measured value instead of the accepted/theoretical value when calculating percent error is a common formula mix-up — the standard convention specifically uses the accepted value as the denominator, and using the wrong one produces a numerically different result that doesn't match the conventional definition other sources and instructors expect.