A percentage point is the plain difference between two percentages. A percent change is that difference measured relative to where you started. An interest rate going from 4% to 5% has risen by 1 percentage point, which is a 25% increase in the rate.
Both statements are true at the same time, and that is exactly why the distinction matters. News reports, bank letters and exam results switch between the two, sometimes carelessly and sometimes on purpose, because “up 25%” sounds dramatic and “up 1 point” sounds small.
The two calculations
Start with two percentages, an old one and a new one.
Change in percentage points = New % − Old %
Percentage change = (New % − Old %) ÷ Old % × 100
The first is a subtraction. The second is the ordinary percentage change formula, applied to numbers that happen to be percentages themselves.
| Change in the rate | In percentage points | As a percentage change |
|---|---|---|
| 2% → 3% | +1 points | +50% |
| 4% → 5% | +1 points | +25% |
| 5% → 4% | −1 points | −20% |
| 10% → 12% | +2 points | +20% |
| 20% → 25% | +5 points | +25% |
| 40% → 50% | +10 points | +25% |
| 60% → 45% | −15 points | −25% |
Notice the last row. A fall from 60% to 45% is 15 points, but a 25% drop. And look at the second and third rows together: a rise from 4% to 5% is +25%, while the fall back from 5% to 4% is only −20%, even though both are a single point. Percentage changes depend on the starting value; point changes do not.
Where you will meet the difference
Interest rates
When a central bank raises its rate from 5.25% to 5.50%, that is a rise of 0.25 percentage points, often called 25 basis points (a basis point is a hundredth of a percentage point). For a borrower, the relevant question is what it does to their payment, and that depends on the loan, not on either headline figure. The loan calculator shows the effect on a monthly payment directly.
Polls and elections
If a party’s support goes from 30% to 33%, it has gained 3 points. Saying “support rose 10%” is also correct (3 ÷ 30), but readers often hear it as 30% becoming 40%. Pollsters and most careful reporters use points for exactly this reason.
Exam results and pass rates
A school whose pass rate rises from 80% to 84% has improved by 4 points, or 5%. A school going from 40% to 44% has also improved by 4 points, but that is a 10% improvement. The point change shows how many more students out of every hundred passed; the percentage change flatters schools that started lower.
Risk and medicine
“Doubles your risk” is a percentage change of +100%. If the risk was 1 in 10,000 and is now 2 in 10,000, the change in percentage points is 0.01. Both numbers are correct, but only the second tells you how worried to be. This is the difference between relative and absolute risk, and it is the same arithmetic.
Tax and discount rates
A sales tax going from 8% to 10% is a 2-point rise. On a 50 purchase, the tax goes from 4 to 5, so what you pay rises by 1, which is 2% of the price. Here the point change maps directly onto the extra cost as a share of the price, which is why points are usually the more useful figure for rates applied to a base.
How to tell which one a sentence means
- “Rose by 2 points” / “2 percentage points” — subtraction. 10% became 12%.
- “Rose by 2%” — strictly, a relative change. 10% became 10.2%. In practice many writers mean points, so check the actual before-and-after figures if they are given.
- “Rose to 2%” — that is the new level, not a change at all.
- “Basis points” (bps) — hundredths of a percentage point. 50 bps = 0.5 points.
When you write about changes in rates yourself, say “percentage points” for the subtraction and give both the old and new figures. Nobody can misread “from 4% to 5%”.
A quick worked example
A savings account paid 3.2% last year and pays 4.0% now.
- Change in points: 4.0 − 3.2 = 0.8 percentage points.
- Percentage change in the rate: 0.8 ÷ 3.2 × 100 = 25%.
- On a 10,000 balance, annual interest goes from 320 to 400: 80 more a year, which is also 25% more interest. The percentage change in the rate is the percentage change in the interest, because the balance did not change.
That last line is the useful insight: when the base stays fixed, a percentage change in a rate is the percentage change in what the rate produces. When the base changes too, you need to recompute from the actual amounts.
Common mistakes
- Adding a percentage change to a rate. A 5% rate “rising by 10%” becomes 5.5%, not 15%.
- Reversing a change with the same percentage. Up 25% then down 25% does not return you to the start. See reverse percentages for why.
- Comparing percentage changes from different starting levels. A 50% jump from 2% and a 10% jump from 10% are the same one-point move.