The percent error formula
Percent error expresses the gap between a measurement and the true value as a percentage of that true value:
Percent error = |Measured − Actual| ÷ |Actual| × 100
A measured value of 9.8 against a true value of 10 has an absolute error of 0.2, so the percent error is 0.2 ÷ 10 × 100 = 2%. The signed difference, −0.2, shows the measurement came in low.
Absolute, relative, and signed
- Absolute error: the raw size of the miss — |measured − actual|.
- Relative error: absolute error ÷ actual, as a decimal (percent error is this × 100).
- Signed difference: measured − actual, keeping the sign so you know the direction.
Reading the result
Lower percent error means a more accurate measurement. What counts as "good" depends on the field — under 5% is often solid for a lab experiment. For comparing percentages in general, see the percentage calculator.
Frequently asked questions
What is the percent error formula?
Percent error is the size of the difference between a measured value and the true value, divided by the true value, as a percentage: |measured − actual| ÷ |actual| × 100. A measured 9.8 against a true 10 is |−0.2| ÷ 10 × 100 = 2%.
How is percent error different from percent difference?
Percent error compares a measurement to a known correct value, so there is a clear "right" answer in the denominator. Percent difference compares two values when neither is the reference, dividing by their average instead.
Can percent error be negative?
The standard percent error uses absolute value, so it is reported as a non-negative number. The signed difference (measured − actual) does carry a sign, telling you whether your measurement was too high or too low — the calculator shows both.
What is a good percent error?
It depends entirely on the context. In a careful lab experiment, under 5% is often considered good and under 1% excellent. For rough field estimates a larger error may be acceptable. Lower is always better, since it means your measurement is closer to the truth.
Which value goes in the denominator?
The true, accepted, or theoretical value — not your measurement. Dividing by the correct value is what makes the error meaningful. If you divide by the measured value instead, you get a slightly different figure that is not standard percent error.
Disclaimer: Percent error is undefined when the true value is zero. Results are provided for educational purposes.