Percent error measures how far a measurement is from the true value. The formula is: percent error = (|measured − actual| ÷ |actual|) × 100. The absolute-value bars keep the result positive so you can compare the size of errors regardless of direction.
Worked example: a lab measurement
A scale should read 250 g but shows 245 g. Subtract: 245 − 250 = −5. Take the absolute value: 5. Divide by the actual value: 5 ÷ 250 = 0.02. Multiply by 100: 2% error. The measurement is 2% off the true value.
Worked example: an overestimate
A temperature sensor reads 103.4 °C when the true temperature is 100 °C. The difference is 3.4, and 3.4 ÷ 100 = 0.034, giving a 3.4% error. Overshooting and undershooting give the same magnitude of error, because the sign is dropped by the absolute value.
Worked example: comparing two experiments
You measure a length as 49 cm when it is 50 cm: error = 1 ÷ 50 = 2%. A second experiment measures 19.6 cm when it is 20 cm: error = 0.4 ÷ 20 = 2%. Both have the same 2% error, which is why percent error is fairer than a raw difference when quantities have different sizes.
Percent error at a glance
| Actual | Measured | Difference | Percent error |
|---|---|---|---|
| 250 | 245 | 5 | 2% |
| 100 | 103.4 | 3.4 | 3.4% |
| 80 | 76 | 4 | 5% |
| 200 | 209 | 9 | 4.5% |
Percent error vs percentage difference
Percent error needs a known true or accepted value, and it divides by that value. Percentage difference is used when neither value is more correct than the other; it divides by the average of the two. If there is an accepted answer to compare against, use percent error. If you are simply comparing two peer measurements, use percentage difference.
Sign, rounding and reporting
Because of the absolute-value bars, percent error is normally reported as a positive number. Some textbooks keep the sign to show direction, calling a reading above the true value a positive error and one below it negative. Decide which convention your class or report uses and stay consistent. Round the final percentage to one or two decimals unless a stricter precision is required, and always state the true value you compared against, since the denominator defines the meaning of the result.
Where percent error is used
Percent error is standard in science labs, engineering tolerance checks, manufacturing quality control and statistics. It answers a simple, practical question: how good is this measurement compared with the real thing? A result under 5% is often considered acceptable in school experiments, while industrial processes may need errors below 1%.
To compare two numbers that both carry uncertainty, use our percentage difference calculator, and read percentage difference vs percentage change for the full distinction.