- Percentage error
- 2%
- Signed error
- -0.2
How it works
Small references amplify relative errors
An observed 0.02 against a reference of 0.01 gives 100% error, although the absolute gap is only 0.01 units. Report the absolute difference too when a reference near zero makes percentages look disproportionately large.
Choosing the reference value for percent error
Percent error compares a measured or estimated value with a reference value. The reference belongs in the denominator, so swapping the two values changes the meaning of the answer. Check the selected formula's treatment of the sign and absolute difference. If the reference is zero, a relative percentage cannot be interpreted in the same way as an ordinary nonzero comparison.
Percentage error: formula and assumptions
Percent error = |observed − accepted| ÷ |accepted| × 100%.
The accepted value must be nonzero. Signed error is also shown.
Worked example
Using the Percentage error example:
- Experimental value
- 9.8
- Accepted value
- 10
Percent error = |observed − accepted| ÷ |accepted| × 100%.
Example result
Percentage error: 2%
Signed error: -0.2
These are illustrative inputs. Change the values to explore a different scenario.
Formula references
References explain the underlying methods; they do not imply endorsement or individual professional review of Finflo.
Common questions
Why must the accepted value be nonzero?
Percentage error divides by the magnitude of the accepted value. A zero reference makes that relative comparison undefined.
What does signed error add to absolute percentage error?
Absolute percentage error describes the size of the discrepancy. Signed error also preserves whether the observation lies above or below the reference.
Prepared by Finflo. See our methodology and editorial policy.