How this calculator works
- Step 1DifferenceO − EHow far the measurement is from the expected value.
- Step 2Size only|O − E|Ignore whether it is over or under.
- Step 3Percent error÷ |E| × 100As a share of the expected value.
Percent error tells you how far an experimental result is from the accepted value, as a percentage of that value. Smaller is closer.
The calculator also shows the signed difference, so you can see whether the measurement was too high or too low.
Worked example: 48.7 g against 50 g
- Percent error
%E = |O − E| ÷ |E| × 100
- OObserved value 48.7 g
- EExpected value 50 g
- Difference48.7 − 50−1.3 g
- Size|−1.3|1.3 g
- Percent error1.3 ÷ 50 × 1002.6%
These are the numbers in OpenStax Contemporary Mathematics, Exercise 24. Exercise 25, gravity measured as 9.457 m/s² against 9.807 m/s², gives 3.568879%.
Over or under
- Under−2.6%48.7 against 50: the measurement is low.
- Over+5%105 against 100: the measurement is high.
Read the result
The headline is the percent error, always zero or more; the signed difference beneath it shows the direction.
What counts as acceptable depends on the experiment and the instruments. Many school practicals treat a few percent as good agreement, but check your own guidance.
Assumptions and limits
- Same unitBoth values must use the same unit.
- Expected not zeroPercent error divides by the expected value.
- Six decimalsRounded for display only.
Related percentage tools
Percent error compares a measurement with an expected value. Other percent questions use a different base.
For percentage change, shares and original values, use the percentage calculator. To report a measured value to the right precision, the significant figures calculator counts and rounds figures.
Common mistakes
Mistake: Dividing by the observed value.
Instead: Divide by the expected (accepted) value.
Mistake: Reporting a negative percent error.
Instead: Percent error uses the size; give direction separately.
Mistake: Mixing grams and kilograms.
Instead: Convert both values to the same unit first.
Checking the method
Every golden case is re-solved with exact fractions using the ratio of observed to expected.
An independent script computes (O ÷ E − 1) × 100 exactly and compares it with every result.
Read how we test our calculators, or browse more maths calculators.