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 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.
The meaning of percent error follows from the relationship, so a different setup can produce a valid answer to a different question.
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.
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%.
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.
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.
Review the sign, scale, and unit of percent error after entering observed or experimental value and accepted or reference value.
The cleanest input audit is to restate the problem using observed or experimental value and accepted or reference value. If that sentence sounds wrong, correct the assignment before asking for percent error.
The same raw error produces a larger percentage when the accepted magnitude is small. Reversing observed and accepted values generally changes the percentage because the reference denominator changes. The pattern also provides a quick estimate of whether a revised result is plausible.
The formula and result serve different readers: the formula shows what was done, and the rounded percent error communicates scale. Keep both when the work needs review.
Use percent error when one value is accepted as the reference. For two peer measurements without a reference, a symmetric percentage-difference formula avoids privileging either one. The wording of the problem should decide which operation is appropriate.
A screenshot is unnecessary when observed or experimental value and accepted or reference value and the shown formula are saved in plain text. Include the rounding rule if the reported percent error is approximate.
Yes. An error larger than the accepted magnitude produces a result over 100%.
Division by zero is undefined, so the conventional percent-error formula cannot scale the difference.
No. Absolute value removes direction; signed relative error is needed to distinguish high from low.
Usually not. Keep measured precision through the calculation and round the final percentage appropriately.
No. Percentage difference treats both values symmetrically and commonly divides by their average.