Percent Error Formula
Percent error tells you how far a measured or estimated value is from the accepted (true or theoretical) value, as a percentage of the accepted value. It is widely used in chemistry and physics labs to judge the accuracy of an experiment.
Percent error = |Measured − Accepted| ÷ |Accepted| × 100%
The absolute value makes percent error positive regardless of whether the measurement was too high or too low. Some teachers use the signed version, (Measured − Accepted) ÷ |Accepted| × 100%, to show the direction of the error; this calculator shows both.
Worked Example
A student measures the acceleration due to gravity as 9.6 m/s². The accepted value is 9.81 m/s².
- Absolute error = |9.6 − 9.81| = 0.21
- Percent error = 0.21 ÷ 9.81 × 100 = 2.14%
- Signed error = −2.14% (the measurement was too low)
Percent Error vs. Percent Difference vs. Percent Change
- Percent error compares a measurement with a known correct value.
- Percent difference compares two values when neither is the reference, dividing by their average.
- Percent change compares a new value with an old value, dividing by the old value.
Why the Accepted Value Cannot Be Zero
Percent error divides by the accepted value, so it is undefined when that value is 0. In that case, report the absolute error instead.
Frequently Asked Questions
What is the formula for percent error?
Percent error = |measured − accepted| ÷ |accepted| × 100. For a measurement of 9.6 when the accepted value is 9.81, the percent error is 2.14%.
Can percent error be negative?
The standard formula uses absolute value, so it is never negative. A signed percent error can be negative, meaning the measured value was below the accepted value.
What is a good percent error?
It depends on the experiment. In many introductory lab courses, errors under about 5% are considered good, but precision instruments may require far less than 1%.
Can percent error be more than 100%?
Yes. If the measured value is more than double the accepted value (or far below it with a sign change), the percent error can exceed 100%.
What is the difference between absolute and relative error?
Absolute error is the raw difference, |measured − accepted|, in the original units. Relative error divides that by the accepted value; multiplying relative error by 100 gives percent error.