Percentage difference vs. percent change
Both describe how far apart two numbers are, but they answer different questions, and mixing them up is one of the most common percentage errors.
| Percent change | Percentage difference | |
|---|---|---|
| Question | How much did it grow or shrink? | How different are these two? |
| Divides by | The starting value | The average of both |
| Order matters? | Yes, and it can be negative | No, it's always positive |
| 40 vs 60 | +50% (40→60) or −33.33% (60→40) | 40% |
| Good for | Prices over time, salaries, growth | Two shops, two quotes, two measurements |
How percentage difference is calculated
- Find the gap: subtract one value from the other and ignore the sign.
- Find the average of the two values.
- Divide the gap by the average and multiply by 100.
Example: one contractor quotes $4,200 and another quotes $5,000. The gap is $800 and the average is $4,600, so the quotes differ by 800 ÷ 4,600 × 100 = 17.39%. Neither quote is the "original", so this is fairer than saying the second is 19.05% higher or the first is 16% lower, although both of those statements are also true.
Percentage points: when the numbers are already percentages
When you compare two rates, such as interest rates, test scores or election results, there are two ways to describe the move, and the news often blurs them.
- Percentage points are the simple subtraction: a savings rate going from 4% to 5% is up 1 percentage point.
- Percent change is relative: the same move is a 25% increase in the rate, because 1 is 25% of 4.
Tick "Both values are already percentages" above and the result shows both, so you can quote whichever one you mean.
Which number should be A?
For percentage difference it doesn't matter. For percent change, put the earlier or reference value in A. If you're asking "how much more expensive is store B than store A", A is the reference. If there is no natural reference, report the percentage difference instead. If you only need the change in one direction, the percentage increase calculator gives a cleaner answer.
Questions people ask
What is the formula for percentage difference?
Divide the absolute difference between the two values by their average, then multiply by 100: |a − b| ÷ ((a + b) ÷ 2) × 100. For 40 and 60 that is 20 ÷ 50 × 100 = 40%.
When should I use percentage difference instead of percent change?
Use percent change when one value clearly comes first, like a price last month and this month. Use percentage difference when the two values are on equal footing, like two stores, two lab measurements or two quotes.
Why do I get a different answer depending on which number I start with?
Percent change divides by the starting value, so swapping the numbers changes the result: 40 to 60 is +50%, but 60 to 40 is −33.33%. Percentage difference divides by the average, so the order doesn’t matter.
What are percentage points?
Percentage points are the plain gap between two percentages. A mortgage rate moving from 6.5% to 7% rose by 0.5 percentage points, which is a 7.69% increase in relative terms.
Can percentage difference be over 100%?
Yes, up to a maximum of 200%, which happens when one value is zero and the other isn’t. 10 and 90 have a percentage difference of 160%.