Difference is not the same as change
Two numbers can be compared in percentages in two genuinely different ways, and mixing them up produces arguments in news reports, lab results and price negotiations. Percentage change is directional: it asks how much a value grew or shrank from a starting point. Percentage difference is symmetric: it asks how far apart two values are, without declaring either one the starting point. This calculator gives you the percentage difference as the headline, and both directional changes alongside it, so you can use the right one and see all three at a glance.
The percentage difference formula
Take the absolute difference between the two values — the minus sign is ignored, so the order never matters — and divide it by their average. Using the average as the base is what makes the measure symmetric: the percentage difference between 100 and 120 is the same as between 120 and 100. Compare that with percentage change, whose formula divides by the starting value only: change = (new − old) ÷ old × 100.
A concrete contrast
Going from 100 to 120 is a +20% change (20 divided by the starting 100). Coming back from 120 to 100 is a −16.67% change (20 divided by the starting 120). Neither is wrong — they answer different questions. The percentage difference between 100 and 120 sidesteps the direction entirely: difference 20, average 110, so 20 ÷ 110 × 100 = 18.18%. Notice it sits between the two change figures, which it always does when the values are positive.
When to use which
Use percentage difference when comparing two measurements, two methods, two quotes or an experimental result against a reference value — anywhere neither number is naturally the before picture. Scientists comparing two instruments and shoppers comparing two estimates are in this territory. Use percentage change when time or direction is real: prices over a year, weight over a diet, revenue quarter to quarter. If a headline percentage does not say which base it used, be suspicious — choosing the smaller base makes any gap look bigger.
There is one edge case to know about: percentage difference is designed for positive quantities such as prices, measurements and counts. When values can be negative — temperatures in Celsius, bank balances, elevations — the average of the two values can approach zero or turn negative, and the percentage stops being meaningful even though the arithmetic still produces a number. In those cases report the plain difference in the original units, and save percentages for the quantities where a zero point genuinely means none.
Worked example
Compare 80 and 100. The difference is 20 and the average is 90, so the percentage difference is 20 ÷ 90 × 100 = 22.22%. The change from 80 to 100 is +25%, and from 100 back to 80 is −20% — three different percentages describing the same pair of numbers, each correct for its own question.
How to use this calculator
- Enter the first value as A.
- Enter the second value as B — order does not matter for the headline result.
- Read the percentage difference in the green panel.
- Check the two percentage change figures if direction matters for your question.
- Follow the step-by-step panel to see the difference, average and division with your numbers.
Percentage points are different again
If a rate moves from 10% to 12%, that is a rise of 2 percentage points, but a 20% percentage increase in the rate itself (2 ÷ 10 × 100). Confusing points with percent is one of the most common errors in reporting interest rates, tax rates, poll results and exam scores. As a rule: subtracting one percentage from another gives percentage points; dividing a change by a starting value gives a percentage change; dividing a difference by an average gives a percentage difference, which is what this page calculates.