What percentage difference actually measures
Percentage difference compares two values without treating either as the starting point. Take the gap between them, divide by their average, and multiply by 100.
For 40 and 60 the gap is 20 and the average is 50, so 20 ÷ 50 × 100 = 40%. Swap the values round and nothing changes, which is the whole point: the result is symmetric, so neither value gets to be the privileged "original". That makes it the right tool for side-by-side comparisons where before and after simply do not apply.
Enter any two values above and the calculator shows the percentage difference along with the raw gap and the average it was measured against, so you can see exactly how the figure was built. It copes with decimals and negative numbers, and warns you in the one situation where the maths genuinely breaks down.
Worked examples
Percentage difference vs percentage change
Percentage change has a direction, because it divides by the starting value. Going from 40 to 60 is a 50% increase (20 ÷ 40), but going from 60 to 40 is a 33.3% decrease (20 ÷ 60). Same two numbers, two different answers, and both are correct for their direction of travel. Percentage difference sidesteps the question by dividing by the average, giving 40% whichever way round you look.
The rule of thumb: if one value clearly came first (last year's price, your old salary, the reading before the change), use percentage change. If the two values are simply alternatives (two quotes, two shops, two brands), use percentage difference. Our percentage change calculator covers the first case.
When the formula misbehaves
Percentage difference assumes both values sit on the same side of zero. If the two values average out to zero (say 50 and −50), the formula divides by nothing and the result is undefined, so the calculator tells you rather than inventing a number. And when the average is very small, tiny gaps produce enormous percentages: 0.1 and 0.3 differ by 100%, which is technically true but rarely useful.
One more cousin worth knowing: percentage error, used in science, divides the gap by the accepted true value rather than the average, because there the "right" answer genuinely is the baseline. A GCSE physics student comparing a measured 9.6 m/s² against the accepted 9.8 m/s² would report a 2% error (0.2 ÷ 9.8 is roughly 0.0204), not a percentage difference. For everyday comparisons of prices, quotes and measurements, though, the average-based formula on this page is the standard one, and it is the version examiners and statistics textbooks mean when they say percentage difference.
Frequently asked questions
What is the formula for percentage difference?
Take the absolute difference between the two values, divide it by their average, then multiply by 100. For 40 and 60 that is 20 ÷ 50 × 100 = 40%. The order of the two values makes no difference to the result.
What is the difference between percentage difference and percentage change?
Percentage change measures movement from a starting value, so it has a direction: from 40 to 60 is a 50% increase, but from 60 to 40 is a 33.3% decrease. Percentage difference divides by the average instead, giving the same 40% whichever way round you compare. Use change for before and after, difference when neither value is the baseline.
Why divide by the average?
Because neither value is the original, the fairest yardstick is the midpoint between them. Dividing by the average makes the result symmetric, so comparing a with b gives exactly the same answer as comparing b with a.
Can percentage difference be more than 100%?
Yes. Comparing 10 and 90 gives a gap of 80 against an average of 50, which is 160%. Any pair of values whose gap is bigger than their average will exceed 100%.
When should I use percentage difference?
When you are comparing two things side by side and neither is the starting point, such as two quotes, two prices in different shops or two salaries. If one value clearly came first in time, percentage change is usually the better measure.