Percentage error measures how far an observed or experimental value is from an accepted value. It expresses the difference as a percentage of the accepted value, making results of different sizes easy to compare.
Percentage error formula
Percentage error = |Observed value − Accepted value| ÷ |Accepted value| × 100
The vertical bars mean absolute value, so the final percentage is normally positive. The accepted value must not be zero because division by zero is undefined.
How to calculate percentage error
- Subtract the accepted value from the observed value.
- Use the absolute value of the difference.
- Divide by the absolute accepted value.
- Multiply by 100 and add the percent sign.
Example: a measured length
A student measures an object as 19.4 cm, while its accepted length is 20 cm. The absolute difference is |19.4 − 20| = 0.6. Divide 0.6 by 20 to get 0.03, then multiply by 100. The percentage error is 3%.
Example: an estimate above the accepted value
Suppose an estimate is 525 and the accepted value is 500. The difference is 25. Therefore, 25 ÷ 500 × 100 = 5%. The same formula works whether the observation is above or below the accepted value.
Percentage error vs percentage difference
Percentage error compares a measured value with a known or accepted reference. Percentage difference compares two values when neither is considered the correct one; it divides their absolute difference by their average. Use our guide to calculate percentage difference when you are comparing two equal-status values.
Signed percentage error
Some fields keep the sign to show direction. Using (observed − accepted) ÷ accepted × 100 produces a positive result for an overestimate and a negative result for an underestimate. Check the convention required by your teacher, laboratory, or report.
Common mistakes
- Dividing by the observed value instead of the accepted value.
- Forgetting to multiply the decimal result by 100.
- Removing the sign when a signed error is specifically requested.
- Rounding during intermediate steps instead of at the end.
- Using percentage error when no accepted reference exists.
Frequently asked questions
Can percentage error be greater than 100%?
Yes. It exceeds 100% when the absolute error is larger than the accepted value.
Is a lower percentage error better?
Usually, a smaller error indicates that the observation is closer to the accepted value. Whether it is acceptable depends on the required precision.
How many decimal places should I use?
Keep full precision during the calculation, then round the final percentage to the precision appropriate for the original measurements.
Calculate other percentage changes
For changes over time rather than measurement accuracy, use the percentage calculator or learn how to calculate percentage increase.