Percentage error is often used when comparing an observed or experimental value with an accepted or reference value.
Percentage Error Formula
A commonly used formula is:
Percentage Error = (|Observed Value − Accepted Value| ÷ |Accepted Value|) × 100
Suppose an experiment produces a value of 98 while the accepted value is 100.
Difference:
|98 − 100| = 2
Then:
(2 ÷ 100) × 100 = 2%
The percentage error is 2%.
Another Example
Observed value = 47.5
Accepted value = 50
Difference:
|47.5 − 50| = 2.5
Then:
(2.5 ÷ 50) × 100 = 5%
Percentage error = 5%.
For the arithmetic involved in percentage calculations, you can use the Percentage Calculator.
Why Absolute Value Is Used
Using the absolute difference expresses the magnitude of the error as a positive percentage. Depending on the field or methodology, signed percentage errors may also be used, so always follow the convention required for your specific analysis.