Percentage Difference Calculator
How far apart two numbers are, in percent, with neither one as the starting point.
Good to know. Percentage difference compares two equals. Percentage change needs a before and an after.
How it works
In plain words
Take the gap between the two numbers and divide it by their average, then multiply by 100. Because the average sits between them, the answer is the same whichever number you enter first.
The formula
percentage difference = |a − b| ÷ ((a + b) ÷ 2) × 100
Worked example
40 and 60 are 20 apart, and their average is 50, so the percentage difference is 20 ÷ 50 × 100 = 40%.
Sources
No outside data or rates: this is plain arithmetic.
5 automated tests check its answers on every change.
About the percentage difference calculator
Percentage difference tells you how far apart two numbers are, relative to their size, when neither is the “before” or the “original”. It is the right measure for comparing two shops’ prices, two measurements of the same thing, two runners’ times or two companies’ results.
The gap is divided by the average of the two numbers, so the result is symmetrical: 40 and 60 are 40% apart, and so are 60 and 40. That is the key difference from percentage change, which divides by the starting value and therefore depends on direction. Going from 40 to 60 is a 50% increase; going from 60 to 40 is a 33.3% decrease; the percentage difference between them is 40% either way.
Use percentage change when there is a clear before and after: a price rise, a salary increase, growth over a year. Use percentage difference when you are comparing two things side by side. In science classes it is also used to compare two experimental results, while percent error compares a measurement with a known true value.
The formula needs the average to be something other than zero, so it can’t compare a number with its negative (5 and −5). For numbers with very different signs or sizes, the plain difference shown below the result is often more useful.
Questions people ask
How do I calculate the percentage difference between two numbers?
Divide the difference by the average of the two numbers and multiply by 100. For 40 and 60: 20 ÷ 50 × 100 = 40%.
Is percentage difference the same as percentage change?
No. Percentage change divides by the starting value, so it depends on which number came first. Percentage difference divides by the average and gives the same answer either way.
Can the percentage difference be more than 100%?
Yes, up to 200%, when one number is far larger than the other. 1 and 99 are 196% apart.