Formula
percentage error = |measured − true| ÷ |true| × 100
- Signed error = (measured − true) ÷ |true| × 100
- The true value must not be zero
The size of your mistake, as a share of the true value.
Worked example
Measuring g as 9.6 instead of 9.81
- Measured (experimental) value
- 9.6
- True (accepted) value
- 9.81
Percentage error
2.140673%
Signed error: −2.140673%
Absolute error: 0.21
Direction: Under the true value
How it works
Percentage error compares a measurement with the value it should have had. Subtract the true value from your measured value, take the absolute value to get the absolute error, divide by the true value and multiply by 100. Measuring g as 9.6 m/s² against the accepted 9.81 gives an error of 0.21 ÷ 9.81 × 100 ≈ 2.14%.
Textbooks differ on whether to keep the sign. Some report a positive percentage error always, and others keep the sign to show whether you were over or under; the calculator gives both so you can match your course. The true value is the denominator, so it cannot be zero.
This is different from a percentage change between two values — for that use the Percentage Change Calculator, and for how far apart two values are with neither being the reference use Percentage Difference Calculator. For repeated measurements the Standard Deviation Calculator describes how spread out they are.
Assumptions and limits
- The true value is treated as exact.
- Both the absolute and the signed error are shown because conventions differ.