Two ways to describe the same change
Percentage points measure the simple difference between two percentages. You subtract one from the other.
Percent change measures how big that difference is compared with where you started. You divide the difference by the starting value.
Example: a savings rate from 4% to 5%
The difference is 5 − 4 = 1 percentage point. Compared with the starting rate, that is 1 ÷ 4 × 100 = 25%. So the bank can truthfully say the rate is "up 1 point" or "up 25%". The second sounds far more impressive.
More examples
| Situation | Points | Percent change |
|---|---|---|
| Mortgage rate 6% → 7% | +1 point | +16.7% |
| Approval rating 40% → 50% | +10 points | +25% |
| Sales tax 8% → 6% | −2 points | −25% |
| Test score 80% → 88% | +8 points | +10% |
| Unemployment 3.5% → 4.2% | +0.7 points | +20% |
Notice that the same 1-point move is a bigger percent change when the starting number is small. A rise from 1% to 2% is a 100% increase, while a rise from 20% to 21% is only 5%.
Basis points
In finance, small rate changes are often given in basis points. One basis point is one hundredth of a percentage point, or 0.01%. So 25 basis points is a quarter point, and 100 basis points is a full percentage point. When you read that a central bank raised rates by 25 basis points, a rate of 4.25% became 4.50%.
Common traps
- "Up 50%" headlines. A risk that goes from 2 in 1,000 to 3 in 1,000 is a 50% increase, but it is only 0.1 percentage points. Ask for both numbers before you judge how big a change is.
- Ups and downs don't cancel. A price that drops 50% and then rises 50% is not back where it started. $100 falls to $50, then rises to $75. The rise is figured on the smaller base.
- Adding percent changes. Two 10% raises do not make 20%. $50,000 × 1.10 × 1.10 = $60,500, a 21% increase overall.
- Percent of what? "Saves 30%" means nothing until you know 30% of which price. Always find the base.
How to say it correctly
If you are comparing two percentages, say "points" for the subtraction and "percent" for the relative change. For example: "The interest rate rose 1 percentage point, from 4% to 5%, a 25% increase." Giving the starting and ending values makes the meaning clear no matter which term the reader expects.