An interest rate goes from 4 per cent to 5 per cent. Has it risen by one per cent or by 25 per cent?
By one percentage point, and by 25 per cent. The first measures the gap between the two figures; the second measures the change relative to where it started. Both are accurate, they are not interchangeable, and the ambiguity is why the phrase "percentage point" exists at all.
The rule
Subtracting one percentage from another gives percentage points. Dividing the change by the starting percentage gives a per cent change.
- 5% − 4% = 1 percentage point
- 1 ÷ 4 = 25 per cent increase
The percentage points calculator returns both figures side by side, which is usually the clearest way to see that they are describing the same movement.
Why the gap gets so wide at small numbers
The relative change depends entirely on the starting point, and at low percentages the starting point is small, so the division produces a large number. A move from 1 per cent to 2 per cent is one percentage point and a 100 per cent increase. The same one-point move from 50 per cent to 51 per cent is a 2 per cent increase.
This is what makes the choice of wording so consequential in reporting. "Cases doubled" and "cases rose by one percentage point" can describe the identical movement, and a reader hearing only one of them forms a very different impression.
Where it costs money
Mortgage rates are the common case. A lender advertising a rate "one per cent lower" than a competitor might mean one percentage point, which on a large balance over decades is an enormous sum, or one per cent of the rate itself, which on a 6 per cent rate is a reduction to 5.94 per cent and is worth almost nothing.
Fees behave the same way. A platform raising its fee from 0.4 per cent to 0.5 per cent has added 0.1 of a percentage point and 25 per cent to what you pay it every year. The first framing sounds like a rounding adjustment; the second is what shows up on the statement.
Reading a claim carefully
If a figure describes a change in something that is already a percentage, ask which of the two is meant before doing anything with it. Percentage points are the safer default for stating a change, because they cannot be inflated by choosing a small base, and the per cent change is the better figure for judging how large the movement is compared with what was there before.
For changes in ordinary quantities, where nothing is a percentage to begin with, the question disappears and the percentage change calculator is all you need.