Percent Difference Calculator
For comparing two values where neither is the original. Divides by their mean, so the order you enter them makes no difference.
Percent difference between two values
Mean of the two
50
Percent change, first to second
+50%
The two figures differ because they answer different questions. Percent difference divides by the mean. Percent change divides by the first value.
Percent difference
40%
|40 − 60| ÷ 50 × 100
The percent difference formula
Percent difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
The gap between the two values, divided by their average, as a percentage. It is always zero or positive, and it gives the same answer whichever way round you enter the numbers.
Worked example — 40 and 60
|40 − 60| = 20
(40 + 60) ÷ 2 = 50
20 ÷ 50 = 0.4
0.4 × 100 = 40
So the percent difference is 40%.
Why it is not 50%
Percent change from 40 to 60 is 50%, because it divides the gap of 20 by the starting value of 40. Percent difference divides the same gap by the mean of 50, giving 40%.
Neither is wrong. They answer different questions:
- Percent change — "how far did this move from where it started?" It has a direction and an origin.
- Percent difference — "how far apart are these two?" It has neither.
When to reach for percent difference
Use it whenever calling one value "the original" would be arbitrary:
- Two instruments measuring the same quantity.
- Two lab groups reporting the same experiment.
- Two suppliers quoting for the same job.
- The same measurement repeated, with no expected direction.
If one of your values is a known correct answer, you want percent error instead — that divides by the accepted value, not the mean.
The edge case
Percent difference has no answer when both values are zero, because the mean is zero and the formula would divide by it. Two values that are equal and non-zero give 0%, which is correct.
Common questions
- What is the percent difference formula?
- Percent difference = |a − b| ÷ ((|a| + |b|) ÷ 2) × 100. Divide the gap between the two values by their mean, then multiply by 100.
- Why divide by the mean instead of one of the values?
- Because neither value is the reference. Dividing by the mean treats both symmetrically, so you get the same answer whichever order you enter them.
- Can percent difference be negative?
- No. It measures how far apart two values are, not which is bigger, so it is always zero or positive. If you need a direction, use percent change instead.
- When should I use percent difference rather than percent change?
- Use percent difference when neither value came first — two instruments measuring the same thing, two lab groups, two suppliers' quotes. Use percent change when one value is the original and the other is what it became.