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40%
The difference between 40 and 60 is 40%
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The percent difference formula
Percentage difference = |first − second| ÷ ((first + second) ÷ 2) × 100
How to calculate percentage difference
- 1.Subtract one value from the other and ignore the minus sign. The order does not matter here.
- 2.Add the two values and halve the total to get their average.
- 3.Divide the gap by that average, then multiply by 100.
Worked example
Two shops quote $40 and $60 for the same item. What is the percentage difference?
- The gap is 60 − 40 = 20
- The average is (40 + 60) ÷ 2 = 50
- 20 ÷ 50 × 100 = 40%
A 40% difference. Note that going from 40 to 60 would be a 50% increase, which is a different question.
Why it divides by the average
Neither value is the starting point, so neither has a claim to be the base. Dividing by the average treats them equally, which is why the answer is the same whichever way round you enter them and why it is always positive.
Common questions
What is the difference between percentage difference and percentage change?
Percentage change measures against the first value and has a direction. Percentage difference divides by the average of the two, so it has no direction and never depends on order.
Why is my percentage difference smaller than the percent change?
Because the average is larger than the smaller of the two values. Comparing 40 and 60 gives a 40% difference but a 50% increase, from the same pair of numbers.
When should I use percentage difference?
When you are comparing two measurements, quotes, or results where neither came first. If one value is a starting point, percent change is the right calculation.
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The percent difference formula
Percentage difference = |first − second| ÷ ((first + second) ÷ 2) × 100
How to calculate percentage difference
Subtract one value from the other and ignore the minus sign. The order does not matter here. Add the two values and halve the total to get their average. Divide the gap by that average, then multiply by 100.
Why it divides by the average
Neither value is the starting point, so neither has a claim to be the base. Dividing by the average treats them equally, which is why the answer is the same whichever way round you enter them and why it is always positive.
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