How to Use This Tool
Enter a measurement and the value you are comparing it against. Both percentage error and percentage difference are shown, because choosing between them is the actual decision.
The two formulas
- Percentage error = |measured − true| ÷ |true| × 100. Use it when one value is genuinely authoritative — a specification, a calibrated standard, an accepted physical constant, a known quantity.
- Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100. Use it when neither value has a stronger claim, such as two instruments measuring the same thing.
For 105 against 100 they give 5.00% and 4.88% — close enough that the distinction looks pedantic. It stops looking pedantic as the gap grows.
Percentage error is not symmetric
Compare 100 and 150. If 150 is the reference, the error is 33.33%. If 100 is the reference, the error is 50.00%. The absolute gap is 50 in both cases; only the denominator changed.
This is the same asymmetry that makes percentage change confusing: going up from 100 to 150 is +50%, and coming back down is −33.3%. Nothing has gone wrong, and reporting one figure without saying what it was divided by is a real ambiguity rather than a rounding detail.
Percentage difference is symmetric — 40.00% whichever way round you write it — which is exactly why it exists.
When percentage error breaks down
Two cases where the number stops meaning anything:
- The reference is zero, and the calculation is undefined. There is no percentage version of "the true value was zero and I measured 0.3".
- The reference is near zero, where the percentage explodes without the measurement getting any worse. An instrument accurate to ±0.5 units is 0.5% wrong at 100 and 50% wrong at 1.
In both cases quote the absolute error instead, which is why specifications for small quantities are written as "±0.5 mg" rather than as a percentage. Many instrument specifications combine the two: ±(0.5% of reading + 2 digits), precisely to cover the low end.
Accuracy, precision and significant figures
Accuracy is how close a measurement is to the true value, and it is what this page computes. Precision is how close repeated measurements are to each other, which needs several readings and a standard deviation — a measurement can be highly precise and consistently wrong.
One more habit worth keeping: a percentage error cannot be more precise than the measurements it came from. If both values are given to three significant figures, quoting an error to five decimal places invents certainty that is not there.
