When two numbers are equals
Sometimes neither number is the starting point. Two contractors quote 40 and 50 for the same job. Two scales weigh the same parcel and disagree. Two shops price the same item differently. Asking "what is the percent change?" forces you to pick one as the base, and you get 25% one way and 20% the other.
Percentage difference avoids that by comparing the gap with the average of the two values. The answer is the same whichever number you put first, which makes it the fair way to say how far apart two equal partners are.
Using the calculator
- Enter the first value in Value A and the second in Value B. The order does not change the main answer.
- Read the percentage difference, plus the plain difference and the average it was measured against.
- Check the two percent changes underneath. They show the move from A to B and from B to A, in case you do need a direction after all.
The percent difference formula
percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100The top of the fraction is the gap between the two values, with any minus sign dropped. The bottom is their average. Dividing the gap by the average and multiplying by 100 turns it into a percent.
Because the average sits between the two values, the percent difference always lands between the two percent changes. That is what makes it neutral.
Worked example: two quotes of 40 and 50
- The gap: |40 − 50| = 10
- The average: (40 + 50) ÷ 2 = 45
- The difference in percent: 10 ÷ 45 × 100 = 22.22%
The quotes are 22.22% apart. Compare that with the two percent changes the calculator also lists: going from A to B is a 25% rise, and going from B to A is a −20% change. The percent difference sits between them, as it always does.
If you are choosing between the quotes and want to know how much more the dearer one costs, the 25% figure is the useful one. If you are reporting how closely two estimates agree, use 22.22%.
Which one should I use?
| Situation | Use |
|---|---|
| A price went from one value to another over time | Percent change |
| Two quotes, two scales or two samples, neither one the reference | Percent difference (this page) |
| A measurement against a known true value | Percent error: |measured − true| ÷ true × 100 |
| A part of a total | Percentage of a number |
Science classes often ask for percent error instead. It looks similar, but it divides by the true or accepted value, not the average, because one of the numbers really is the reference.
Things that trip people up
- Reporting a percent difference as an increase. It has no direction, so "B is 22% higher" is wrong. B is 25% higher than A.
- Using it with values on either side of zero. The average of 10 and −10 is 0, so there is no percent difference to speak of. That is why the boxes here take zero and positive numbers only.
- Comparing percentages with percent difference. Two rates of 8% and 10% differ by 2 percentage points; their percent difference is 22.22%. Say which one you mean.
Frequently asked questions
How do I calculate the percentage difference between two numbers?
Find the gap between them, ignoring any minus sign, then divide by their average and multiply by 100. For 40 and 50, the gap is 10 and the average is 45, so 10 ÷ 45 × 100 = 22.22%. Swap the numbers and you get the same answer, which is what makes this measure useful.
Is percentage difference the same as percent change?
No. Percent change compares a new value with an old one, so it has a direction and depends on which number is the base. Percentage difference has no direction and uses the average as the base. From 40 to 50 is a 25% change, but the two values are 22.22% apart.
Can the percentage difference be more than 100%?
Yes, up to a limit. When one value is much larger than the other, the gap can be bigger than the average. For 10 and 50, the gap is 40 and the average is 30, so the difference is 133.33%. The largest it can ever be is 200%, when one of the values is 0.
How is this different from the difference calculator in a spreadsheet?
A spreadsheet minus sign gives you the plain difference, like 10. That number has no sense of scale: a gap of 10 between 40 and 50 is big, but between 4,000 and 4,010 it is tiny. Dividing by the average puts both on the same footing, which is why the percent version is easier to compare.
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