Percentage Difference Calculator
Enter any two numbers to see how far apart they are as a percentage of their average. Neither number is treated as the starting point.
What is the percentage difference between and ?
The gap is 20 and the average is 50.
The percentage difference formula
Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100
The gap between the two numbers is divided by their average, so neither number counts as the starting point. Swap a and b and the answer stays the same.
Worked examples
| A | B | Average | Difference |
|---|---|---|---|
| 40 | 60 | 50 | 40% |
| 100 | 120 | 110 | 18.1818% |
| 15 | 25 | 20 | 50% |
| 8 | 10 | 9 | 22.2222% |
For 100 and 120 the gap is 20 and the average is 110. Divide 20 by 110 to get 0.1818, so the difference is about 18.18%.
Difference or change?
If one number is clearly the original and the other is the result, such as a price before and after a rise, use the percentage increase or percentage decrease calculator. Use percentage difference only when the two numbers are peers.
FAQ
How do you calculate percentage difference?
Find the gap between the two numbers, divide it by their average, then multiply by 100. For 40 and 60 the gap is 20 and the average is 50, so 20 ÷ 50 × 100 = 40%.
What is the percentage difference formula?
Percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100. The vertical bars mean you take the size of the gap and ignore whether it is positive or negative.
What is the difference between percentage difference and percentage change?
Percentage change treats one number as the starting point and divides by it. Percentage difference treats the two numbers equally and divides by their average, so you get the same answer whichever order you enter them.
When should I use percentage difference?
Use it when you are comparing two values with no obvious before and after, such as the prices of two products or the results of two experiments. If one value is the original and the other is the result, use percentage change instead.
Why does 40 and 60 give 40% rather than 50%?
Because the gap of 20 is divided by the average, 50, not by 40. Going from 40 to 60 as a change would be 50%, but as a difference between two equal peers it is 40%.
Can the percentage difference be over 100%?
Yes, if the gap is larger than the average of the two numbers. For example, 10 and 90 have a gap of 80 and an average of 50, which is 160%.
Is percentage difference always the same whichever number I enter first?
Yes. It divides the gap by the average of the two numbers, so swapping them gives the same answer. That is what separates it from percentage change.
What is the percentage difference between 50 and 80?
The gap is 30 and the average is 65, so the difference is 46.15%. As a change, 50 to 80 is a 60% increase.
Why is the maximum percentage difference 200%?
For two positive numbers, the gap can never exceed twice the average. When one number is tiny compared with the other, the gap approaches the full average multiplied by two, so the percentage approaches 200%.
Percentage difference compared with percentage change
The same two numbers can give three different percentages depending on the question you are asking. Percentage difference treats the two values as equals. Percentage change treats one as the starting point.
| A | B | Percentage difference | Change from A to B | Change from B to A |
|---|---|---|---|---|
| 100 | 120 | 18.18% | +20.00% | -16.67% |
| 50 | 80 | 46.15% | +60.00% | -37.50% |
| 8 | 10 | 22.22% | +25.00% | -20.00% |
| 1000 | 1500 | 40.00% | +50.00% | -33.33% |
For 100 and 120 the difference is 18.18%, an increase from 100 to 120 is 20%, and a decrease from 120 to 100 is 16.67%. None of them is wrong: they answer different questions.
What the result looks like at different scales
| A | B | Percentage difference |
|---|---|---|
| 100 | 101 | 1.0% |
| 100 | 110 | 9.5% |
| 100 | 150 | 40.0% |
| 100 | 200 | 66.7% |
| 100 | 500 | 133.3% |
| 100 | 1000 | 163.6% |
The percentage difference is capped at 200% when both numbers are positive, however far apart they are, because it is divided by the average. A change from 100 to 1000 is a 900% increase, but the percentage difference is 163.6%.
When percentage difference is the right choice
- Comparing two similar items, such as two phones' battery capacities, two brands' prices, or the weights of two products.
- Comparing two measurements, such as an experimental value against a second trial, when neither is the true value.
- Comparing two people or groups, such as salaries at two firms or populations of two towns.
When one value is a known reference, such as a measured value against a theoretical one, scientists often use percent error, which divides by the reference value instead of the average.
Common mistakes
- Mixing up percentage difference and percentage points. If a rate moves from 20% to 25%, it rises by 5 percentage points, which is a 25% increase.
- Using percentage difference for before and after. If one number came first, use percentage increase or decrease.
- Comparing negative numbers. The formula divides by the average, which can be zero or near zero for mixed-sign values and gives a misleading result.