Math
Percentage Point Calculator
When a rate moves from 40% to 50%, is that a 10% increase or a 25% increase?
Both, depending on what you mean. Enter two percentages to get the change in percentage points (the simple subtraction) and the relative percent change (the growth of the rate itself), or add a number of points to a starting rate.
The earlier or reference rate, for example 40.
The later rate, for example 50.
Try an example
Result
Result
—
- Relative percent change
- —
- Ratio of the two rates
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- Starting rate
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- Ending rate
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Percentage points versus percent
A percentage point (pp) is the unit for the plain difference between two percentages: 50% minus 40% is 10 percentage points. Percent change treats the starting rate as the base: (50 - 40) / 40 = 25%. News headlines that say a rate 'rose 10%' when it went from 40% to 50% are mixing the two, and the calculator shows both so you can be precise.
| From | To | Percentage points | Percent change |
|---|---|---|---|
| 40% | 50% | +10 pp | +25% |
| 50% | 40% | -10 pp | -20% |
| 2% | 3% | +1 pp | +50% |
| 20% | 20% | 0 pp | 0% |
| 0% | 5% | +5 pp | undefined |
Which one should you report?
Use percentage points when the percentages are rates or shares of the same whole: interest rates, unemployment, approval ratings, market share. Use percent change when you want to express growth of the rate itself, and say so explicitly. Small starting rates make percent change look huge (2% to 3% is a 50% increase but only 1 point), which is why points are the fairer default.
How to use it
- Enter the starting and ending percentages to compare them, or the starting percentage and points to add.
- Read the percentage-point change as the main result and the relative percent change beside it.
- Check the ratio of the two rates when you want to say 'the rate is 1.25 times what it was'.
- Open Show the work to see the subtraction and the division written out.
How to read the answer
The percentage-point figure is the plain gap between the two rates and is what most reports should quote. The relative change tells how much the rate grew or shrank compared with its starting size. When the starting rate is small, the relative change can be large even for a tiny move in points.
Common mistakes and edge cases
- Do not call a 10-point change a '10% increase' unless the rate really grew by 10% of itself.
- Percent change from a 0% starting rate is undefined; only the point change makes sense.
- Points are not symmetric in percent terms: +10 pp from 40% is +25%, but -10 pp from 50% is -20%.
- Basis points are hundredths of a point, not hundredths of a percent of the rate.
- Adding points to a rate is plain addition; multiplying the rate by a percent is a different operation.
Worked examples
40% to 50%
Compare two rates
Result
10 pp
50% to 40%
Decrease
Result
-10 pp
Small base
2% to 3% is +50% relative
Result
1 pp
No change
20% to 20%
Result
0 pp
From zero
0% to 5%
Result
5 pp
Add points
40% + 10 pp
Result
50%
Subtract points
4.5% - 0.25 pp
Result
4.25%
Both zero
0% to 0%
Result
Error
Frequently asked questions
What is a percentage point?+
The unit for the arithmetic difference between two percentages. Going from 40% to 50% is a change of 10 percentage points.
What is the difference between percentage points and percent?+
Points subtract the two rates; percent change divides the difference by the starting rate. 40% to 50% is 10 points but a 25% increase.
How do you calculate percentage point change?+
Subtract the starting percentage from the ending percentage: 50% - 40% = 10 pp.
What are basis points?+
Hundredths of a percentage point. 25 basis points = 0.25 percentage points. Interest-rate moves are often quoted this way.
Why is the percent change so large when the rates are small?+
Because the base is small. Moving from 2% to 3% is only 1 point, but 1 is half of 2, so the relative change is 50%.
Which should I use in a report?+
Percentage points for changes in rates and shares, unless you specifically want to describe growth of the rate itself, in which case label it as relative change.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026