How to use the Percent Difference Calculator
- Enter the first value.
- Enter the second value.
- Read the percent difference, the gap and the average.
- Use the percentage change line if the first value is your starting point.
Formula used
Percent difference = |a − b| ÷ ((a + b) ÷ 2) × 100. Percentage change = (b − a) ÷ |a| × 100.
Worked example
Here is the Percent Difference Calculator worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| First value | 80 |
| Second value | 100 |
| Result | |
| Percent difference | 22.22% |
| Absolute difference | 20 |
| Average of the two values | 90 |
| Percentage change from first to second | 25% |
The formula
Percent difference = |a − b| ÷ ((a + b) ÷ 2) × 100. For 80 and 100 the gap is 20 and the average is 90, so the percent difference is 20 ÷ 90 = 22.22%. Swapping the values, 100 and 80, gives 22.22%, the same.
Equal values give 0%.
Percent difference versus percentage change
Going from 80 up to 100 is a percentage change of 25% (20 ÷ 80), because 80 is the starting value. Going from 100 down to 80 is -20%, so percentage change depends on direction, while percent difference does not.
Use percent difference when the two values are on equal footing, such as measurement against an alternative method. Use percentage change for before-and-after comparisons, as in the percentage change calculator.
Percent error is a third thing
Percent error compares a measurement with a known true value: |measured − true| ÷ |true| × 100. It divides by the true value, not the average. If you have an accepted value, use the percentage error calculator instead.
Choosing the right one matters because the same two numbers give three different percentages depending on what they represent.
Notes
The formula works for any real numbers. If the two values add up to zero, such as -5 and 5, the average is zero, and the percent difference is undefined, so the calculator says so.
When values are negative, the calculation uses the size of the average. It is more meaningful for values that share the same sign and scale.
Worked example: comparing two prices
A shop sells an item for 40 and a rival sells it for 50. The gap is 10 and the average is 45, so the percent difference is 10 ÷ 45 = 22.2%. If you said "the second is 25% dearer" (10 ÷ 40) or "the first is 20% cheaper" (10 ÷ 50), each would be correct from its own starting point, which is why the neutral percent difference is handy when you only want to describe the gap.
Scientists use it to compare two measurements of the same quantity, for example a reading from two instruments, where neither is known to be the true value. When one is a known standard, percent error is the better measure.
Frequently asked questions
What is percent difference?
The gap between two values divided by their average, shown as a percentage.
How is it different from percentage change?
Percentage change divides by the starting value, so it depends on direction. Percent difference divides by the average, so it does not.
Does it matter which value I enter first?
Not for the percent difference. It matters for the percentage change line.
When should I use percent error instead?
When you are comparing a measurement with a known correct value.
Why is the answer undefined sometimes?
If the two values add up to zero, the average is zero and you cannot divide by it.
Can the result exceed 100%?
Yes, when the values are very different, though the symmetric percent difference for two positive numbers stays below 200%.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.