How to use this calculator
Use percentage difference when neither measurement is the original or accepted reference. Dividing the absolute gap by the average treats both measurements equally. This convention suits comparisons of two nonnegative measured quantities; percent error instead compares a measurement against an accepted value.
Difference, change or error?
| Task | Reference | 48 and 52 |
|---|---|---|
| Compare two measurements equally | Average: 50 | Difference: 8% |
| Measure a change from 48 to 52 | Starting value: 48 | Change: about 8.333333% |
| Measured 48; accepted value 52 | Accepted value: 52 | Absolute percent error: about 7.692308% |
Use percentage change when there is an old value and a new value. For absolute percent error, use |measured − accepted| ÷ |accepted| × 100; an accepted value of zero makes that formula undefined. This calculator calculates the symmetric difference, not percent error.
When the average is not the right reference
Do not use this result to report growth over time or accuracy against a known standard. Swapping 48 and 52 still produces 8%, so the result does not say which measurement increased. With one zero and one positive measurement, the result is 200%; two zeros are undefined because their average is zero.
The formula
Worked examples
Compare 80 and 100
Gap = 20; average = 90; 20 / 90 × 100 ≈ 22.222222%.
Compare 100 and 80
The same gap and average give the same 22.222222%.
Compare 0 and 40
Gap = 40; average = 20; the difference is 200%.
Special cases & input limits
Two equal positive measurements give 0%. Two zeros have a zero average, so this formula is undefined. One zero and one positive measurement give 200%. Negative measurements are rejected.
Inputs support a decimal point and scientific notation, up to 30 significant digits and a magnitude of 10⁻²⁰ to 10³⁰, or zero. Select 0–12 display decimal places. Very small or large answers use scientific notation so a nonzero result is not displayed as zero.
A common mistake
Percentage difference is not signed percent change. From 80 to 100 the change is +25%, while the symmetric difference is about 22.22%.
Content updated · Calculation methodology