How it works
Percentage difference compares two values when neither one is the “original”. Instead of dividing by one of them, it divides by their average, so swapping the values gives the same answer. Scientists, engineers and shoppers use it to compare two measurements, two quotes or two prices.
percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100Worked example. Two quotes of 80 and 100: the difference is 20 and the average is 90, so the percentage difference is 20 ÷ 90 = 22.22%. By contrast, 80 → 100 is a +25% change, and 100 → 80 is a −20% change. The percentage difference sits between the two.
Difference vs change
| Question | Use | Divide by |
|---|---|---|
| How much did the price rise? | Percentage change | The old value |
| How different are these two values? | Percentage difference | The average |
| How far is my result from the true value? | Percentage error | The true value |
If there is a clear before and after, use the percentage change calculator instead. Both directions of percentage change are also shown in the results, so you can pick the one you need.
Things to watch
- The result is always positive and never above 200%.
- It is undefined when both values average to zero, for example 5 and −5.
- For values with very different sizes (1 and 100) the result approaches 200%, which may not be intuitive — percentage change may be clearer.
Need “X is what percent of Y”? Use the percentage calculator. For averages of a whole list of numbers, try the average calculator.