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How to use
Percent error compares a measured or estimated value with an accepted reference. The reference value is the denominator, which makes this different from percent difference between two peer measurements.
- Enter the measured or experimental value.
- Enter the accepted/reference value in the same unit.
- Read signed error, absolute error, percent error and the direction relative to the reference.
How it is calculated
Example
Example: measured 9.5 versus accepted 9.81 gives signed error -0.31, absolute error 0.31 and percent error about 3.1600%. The negative sign means the measurement is below the reference.
Important notes
If the accepted reference is zero, conventional percent error is undefined because the denominator would be zero; absolute and signed error still remain meaningful. If neither value is the accepted reference, use percent difference instead.
Worked examples and interpreting results
When a measurement is 102 and its accepted reference is 100, the signed error is +2, the absolute error is 2 and percent error is 2%.
| Case | Calculation | Result |
|---|---|---|
| Signed error | 102 − 100 | 2 |
| Absolute error | |102 − 100| | 2 |
| Percent error | 2 ÷ 100 × 100 | 2 % |
How to check the result
When the accepted reference is zero, percent error is undefined because division by zero is not possible. Do not report it as 0%.
Frequently asked questions
Can percent error be negative?
The absolute percent error shown is non-negative, but the calculator also reports signed error to show over- or under-estimation.
What if the accepted value is zero?
Conventional percent error is undefined because it would divide by zero, so only absolute and signed error are reported.
How is this different from percent difference?
Percent error uses an accepted reference in the denominator; percent difference treats the two values symmetrically.