The identity used by Percent Error
Percent error scales an absolute difference by the magnitude of the accepted value. That scaling makes errors from differently sized measurements easier to compare than raw differences alone.
Math calculator
Percent Error Calculator
Compare an observed value with an accepted value on a percentage scale. Beside percent error, the output shows the operation used to obtain it.
Percent Error inputs
Build the expression
A concrete Percent Error example
An observation of 9.7 against an accepted value of 10 has absolute error |9.7 − 10| = 0.3. Dividing 0.3 by 10 and multiplying by 100 yields 3%.
Subtract observed and accepted values, take the absolute value, divide by the absolute accepted value, and multiply by 100. Retain enough digits until the final rounding step. A hand-worked extension of Percent Error is absolute difference.
Checks that protect a Percent Error result
The denominator is the accepted value, not the observed value or the average of both. If neither measurement is authoritative, percentage difference may be the more suitable symmetric comparison.
How Percent Error reacts to changed inputs
Documenting Percent Error for the next step
Laboratory measurements, manufacturing checks, forecasts, and estimates use percent error when a reference value is available. It describes closeness, not whether the estimate was high or low. A related application of Percent Error is other percentage calculations.
Reviewing the Percent Error case
Rework Percent Error without copying Percent error. Begin with Observed or experimental value and preserve Accepted or reference value. Predict the scale of the Percent Error answer, then compare it with Percent error. Store a changed Accepted or reference value as another Percent Error case.
Validating Percent Error
Challenge Percent error with a nearby value of Observed or experimental value. Leave Accepted or reference value fixed during the Percent Error trial. The direction of the new Percent error should agree with the underlying Percent Error relationship.
Short answers about Percent Error
Can percent error exceed 100%?
Yes. An error larger than the accepted magnitude produces a result over 100%.
Why is accepted value zero rejected?
Division by zero is undefined, so the conventional percent-error formula cannot scale the difference.
Does percent error show direction?
No. Absolute value removes direction; signed relative error is needed to distinguish high from low.
Should I round the inputs first?
Usually not. Keep measured precision through the calculation and round the final percentage appropriately.
Is percent error the same as percentage difference?
No. Percentage difference treats both values symmetrically and commonly divides by their average.