Percent difference formula
Percent difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100 Take the absolute difference between the two values, divide it by the average of their absolute values, and multiply by 100.
How to calculate percent difference
For the values 40 and 60:
- Find the absolute difference: |40 − 60| = 20
- Find the average: (40 + 60) ÷ 2 = 50
- Divide the difference by the average: 20 ÷ 50 = 0.4
- Multiply by 100: 0.4 × 100 = 40%
The two values differ by 40% of their average. Swap them — 60 and 40 — and every step gives the same result.
Percent difference vs percentage change
These are the two most commonly confused percentage calculations, and they answer different questions:
- Percentage change has a direction. Something moved from an original value to a new one, and the change is measured against where it started.
- Percent difference has no direction. Two values are compared side by side, and the gap is measured against their average, so neither one is treated as the reference.
For 150 and 180, the three possible answers look like this:
- 150 → 180 as a percentage change: 20% increase
- 180 → 150 as a percentage change: 16.67% decrease
- 150 and 180 as a percent difference: 18.18%
The percent difference is the same whichever way round you put the numbers. That's exactly why it is useful when neither value is the reference: choosing one value as the denominator would otherwise make the answer depend on an arbitrary choice.
Use percentage change when something changed over time — a price, a population, a score. Use percent difference when comparing two things measured side by side — two shops' prices, two lab measurements, two survey results.
If you need to find a percentage of a single value rather than compare two values, use the Percentage Calculator.
Percent difference examples
| A | B | Difference | Average | Percent difference |
|---|---|---|---|---|
| 40 | 60 | 20 | 50 | 40% |
| 150 | 180 | 30 | 165 | 18.18% |
| 90 | 110 | 20 | 100 | 20% |
| 100 | 120 | 20 | 110 | 18.18% |
| 50 | 75 | 25 | 62.5 | 40% |
| 10 | 20 | 10 | 15 | 66.67% |
| 1 | 2 | 1 | 1.5 | 66.67% |
| 100 | 200 | 100 | 150 | 66.67% |
| 0 | 50 | 50 | 25 | 200% |
| 250 | 300 | 50 | 275 | 18.18% |
Why it tops out at 200%
Percent difference can never exceed 200%. The difference between two values can be at most the sum of their sizes, and dividing that by half the sum gives exactly 2 — that is, 200%. You reach it when one value is zero: 0 and 50 differ by 50, their average is 25, and 50 ÷ 25 is 200%.
That ceiling is a useful sanity check. A percent difference over 200% means something went wrong in the calculation.
Negative values and zero
The textbook formula averages the two values directly. That works for positive numbers, but fails when the values have opposite signs: 5 and −5 average to zero, so the formula divides by zero, and 10 and −9 average to 0.5, giving a meaningless 3,800%.
This calculator averages the sizes of the values instead, (|A| + |B|) ÷ 2. For positive numbers that is identical to the textbook formula, so ordinary results are unaffected. For values of opposite sign it keeps the answer within the 0–200% range, where it means something. If both values are 0 there is nothing to compare against, and the percent difference is undefined.
Percent difference vs percent error
Percent error looks similar but isn't symmetric: it measures how far an experimental value is from an accepted or true value, and divides by the accepted value alone. It's a percentage change with the "correct" answer as the starting point. Use percent error when one value is known to be right; use percent difference when comparing two measurements where neither is the reference.
Frequently asked questions
What is the percent difference formula?
Percent difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
How do I calculate percent difference?
Subtract one value from the other and ignore the sign, work out the average of the two values, divide the difference by the average, and multiply by 100. For 40 and 60: 20 ÷ 50 × 100 = 40%.
Does the order of the numbers matter?
No. Percent difference is symmetric, so 40 and 60 give the same answer as 60 and 40. If the order matters to your question, you want percentage change instead.
Can percent difference be negative?
No. The formula uses the absolute difference, so the result is always zero or positive. A negative figure means a percentage change was calculated instead.
Can percent difference be over 100%?
Yes, up to 200%. It passes 100% when one value is more than three times the other — 10 and 40 differ by 120% — and reaches exactly 200% when one of the values is zero. It can never go higher.