Percent Error
Compare a measured result to the true value and see how far off it is, as a percentage.
Absolute error (measured − actual) = -0.01.
Percent error is |measured − actual| ÷ |actual| × 100. If you measure gravity as 9.8 m/s² when the accepted value is 9.81 m/s², the error is |9.8 − 9.81| ÷ 9.81 × 100 = 0.10% — your result is off by about a tenth of a percent.
What percent error tells you
Percent error measures how close an experimental measurement is to the value everyone accepts as true. You take the gap between your measured value and the actual (accepted) value, express it as a fraction of the actual value, and scale to a percentage. Because it is divided by the accepted value rather than the absolute size of the gap, the same 0.5 mm slip matters far more on a 2 mm object than on a 2 m one.
the actual (accepted) value is always the base; absolute value keeps the result positive
Worked example
You measure the acceleration due to gravity as 9.8 m/s². The accepted value is 9.81 m/s². What is the percent error?
- 1 Find the absolute error. Subtract and take the absolute value: |9.8 − 9.81| = 0.01.
- 2 Divide by the accepted value. 0.01 ÷ |9.81| = 0.00102 (the actual value is the base, never the measured one).
- 3 Multiply by 100. 0.00102 × 100 = 0.10% — a very accurate measurement.
Example measurements and their percent error
Each row uses |measured − actual| ÷ |actual| × 100.
| Measured | Actual | Percent error |
|---|---|---|
| 9.8 | 9.81 | 0.10% |
| 3.14 | 3.14159 | 0.05% |
| 2.65 | 2.70 | 1.85% |
| 99 | 100 | 1.00% |
| 485 | 500 | 3.00% |
| 1.10 | 1.00 | 10.00% |
Percent error vs. percent difference
Percent error compares a result against a known accepted value, so that accepted value is the denominator. Percent difference compares two measurements when neither is the “correct” one, so it divides by their average instead. If you have a textbook or reference figure to check against, you want percent error.
Accuracy is not precision. Percent error reports accuracy — how close you landed to the truth. Precision is how tightly your repeated measurements agree with each other; you can be precise (consistent) yet inaccurate (consistently wrong) if your instrument is miscalibrated.
The base is always the accepted value. Dividing by the measured value instead changes the answer, and a result with no agreed accepted value cannot have a meaningful percent error at all. To revisit the underlying arithmetic, see the percentage calculator.