The short answer
Percent error measures how far a measured or calculated value strays from a known, accepted value, as a percentage: |measured − accepted| ÷ |accepted| × 100%. A gravity experiment that measures 9.7 m/s² against the accepted 9.8 m/s² has a percent error of about 1.02% — small enough to suggest a reasonably accurate measurement, though what counts as "acceptable" depends entirely on the field.
Key takeaways
- The denominator is always the accepted/true value, not the measured one — swapping them gives a different, incorrect answer.
- The absolute value in the formula means percent error is always reported as positive, even when the measured value is lower than accepted.
- Acceptable percent error varies enormously by field — under 1% in analytical chemistry, but 5–10% is often fine in a classroom physics lab.
- Percent error isn't the same as percent difference — percent difference has no "correct" reference value and divides by the average of the two numbers instead.
The percent error formula
Percent error = |measured − accepted| ÷ |accepted| × 100%
The accepted value anchors the calculation — it represents the standard you're measuring against, so it always sits in the denominator regardless of whether your measurement came in above or below it.
Worked example: measuring gravitational acceleration
A physics experiment measures g = 9.7 m/s². The accepted value is 9.8 m/s².
Absolute error = |9.7 − 9.8| = 0.1
Percent error = 0.1 ÷ 9.8 × 100% ≈ 1.02%
A 1.02% error is typically considered quite good for a hands-on lab measurement of gravity, where friction, air resistance, and timing precision all introduce small unavoidable errors.
Percent error vs. percent difference
| Concept | Formula | When to use |
|---|---|---|
| Percent error | |m−a| ÷ |a| × 100% | You have a known correct value to check against |
| Percent difference | |v1−v2| ÷ ((v1+v2)/2) × 100% | Comparing two measurements, neither authoritative |
Common mistakes to avoid
- Dividing by the measured value instead of the accepted value — the accepted value is always the denominator.
- Forgetting the absolute value and reporting a negative percent error, which the formula is designed to prevent.
- Using percent error when neither value is a known "true" standard — that situation calls for percent difference instead.
- Assuming a low percent error always means a sound experiment — a low percent error can still hide a flawed method if errors happen to cancel out.
Related calculators
- Percentage Calculator — handle general percentage-of and percentage-change problems.
- Rounding Calculator — round a percent error result to the right number of significant figures.
- Standard Deviation Calculator — assess the spread across repeated measurements, not just one comparison.
- Confidence Interval Calculator — express measurement uncertainty as a range instead of a single error value.