Percentage difference calculator
Compare two values with a symmetric percentage difference, or switch to percentage change when the starting value matters.
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Result
The symmetric percentage difference between 80 and 100 is 22.222222 %.
Show calculation steps
Divide the absolute gap by the average of the two absolute values. This is symmetric, unlike percentage change; two zeros are treated as identical.
Formula
Calculation steps
- (|80| + |100|) ÷ 2 ≈ 90
- |80 − 100| ÷ 90 × 100 ≈ 22.222222 %
Numbers are displayed to at most 6 decimal places.
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The formula
Percentage difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100. For 80 and 100, the difference is 20 and the average is 90, so the answer is 20 ÷ 90 × 100 ≈ 22.22%.
Because the formula divides by the average, the answer is the same whichever value you enter first.
Difference or change?
Use percentage change when one value clearly comes first or acts as the reference: last year and this year, the list price and the sale price, the budget and the actual spend. From 80 to 100 is a 25% increase, and from 100 to 80 is a 20% decrease.
Use percentage difference when the two values are on an equal footing: two suppliers’ quotes, two measurements of the same thing, the price of one product in two shops. Neither is the baseline, so neither should be the divisor.
Reporting a percentage difference as if it were a change, or the reverse, is a common source of disagreement in reports. If you aren’t sure, say which formula you used.
When it breaks down
When both values are 0 they are identical and the difference is 0. When the two values have opposite signs, the average of their absolute values can be small compared with the gap, and the percentage stops being a useful summary. In that case, report the difference in units.
For lab work where one value is the accepted or true value, you probably want percent error, which divides by the accepted value rather than the average.
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