Percent Error Calculator
Compare a measured value against the true value to find percent error, absolute error and relative error.
How to use this calculator
- 1Enter what you measured and the accepted true value.
- 2Read the percent error; the accuracy figure is simply its complement.
- 3Turn on "keep the sign" when whether you measured high or low matters.
How the calculation works
Percent error = |measured − true| / |true| × 100- measured
- The value your experiment or instrument produced
- true
- The accepted or theoretical reference value
The denominator is always the true value, never the measured one. Dividing by the measurement would make the error depend on how wrong you were, which is circular.
Undefined when the true value is zero. In that case report absolute error only.
Worked example
Measuring gravity as 9.72 against 9.81 m/s²
- 1.Absolute error = 9.72 − 9.81 = −0.09 m/s².
- 2.Relative error = 0.09 ÷ 9.81 = 0.009174.
- 3.Percent error = 0.009174 × 100 = 0.9174%.
- 4.Under 1%, so this is a good result for a school-laboratory pendulum experiment.
Result: 0.9174%
What percent error is actually measuring
Percent error puts a number on how far a measured or calculated result strayed from a known, trusted value, expressed as a share of that trusted value rather than as a raw difference. Saying you were "off by 2" means very different things depending on whether the true value was 4 or 4,000 — percent error normalises for that by dividing the gap by the true value itself.
Where this shows up outside a school lab
Comparing a result to an accepted reference is a routine step across science, manufacturing and quality control.
- Laboratory experiments — comparing a measured physical constant, like the acceleration due to gravity, against its accepted textbook value.
- Manufacturing tolerances — checking how far a produced part’s dimensions drift from the design specification.
- Forecasting and estimation — comparing a predicted figure, such as a sales or weather forecast, against what actually happened.
- Instrument calibration — a consistently large percent error across repeated measurements often signals a miscalibrated scale or gauge, rather than random noise.
Percent error is not the same as percent difference
The two get confused constantly because they look alike, but they answer different questions. Percent error assumes one of the two values is authoritative — the "true" or accepted value — and always divides by that one. Percent difference is for comparing two measurements where neither one is more trustworthy than the other, and conventionally divides by their average instead, so the answer comes out the same regardless of which value you happened to list first.
What this assumes, and where it stops
Assumptions
- The true value is genuinely authoritative — a published constant or an accepted reference.
Limitations
- Undefined when the true value is zero.
- Says nothing about precision. A set of measurements can be consistently repeatable and consistently wrong.
- For comparing two measurements where neither is a reference, percent difference is the correct measure instead.
Common questions
What is an acceptable percent error?
It depends entirely on the field and the equipment. School laboratory work commonly accepts under 5%; analytical chemistry may require under 1%; some engineering tolerances are tighter still. What matters more than the threshold is whether the error is random or systematic.
What is the difference between percent error and percent difference?
Percent error compares a measurement against a known true value, so it measures accuracy. Percent difference compares two measurements where neither is authoritative, and divides by their average so the answer is the same whichever order you enter them.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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