“Interest rates rose from 5% to 6%.” Did rates go up by one percent, or by twenty? Both — and the difference between saying it right and saying it wrong is the kind of mistake that moves markets and misreads elections. Here’s how to never confuse the two again.
Short answer: A percentage point is the raw gap between two percentages (5% → 6% is +1 point). A percent change measures that gap against the starting value (5% → 6% is +20%). When a number is itself a percentage, always say which one you mean.
The trap in one example
A rate moves from 5% to 6%. Two true statements:
- It rose 1 percentage point (6 − 5 = 1).
- It rose 20 percent (the extra 1 is one-fifth of the original 5).
Both describe the identical change. A headline that writes “rates rose 20%” when they only rose one point isn’t lying — it’s using the scarier framing. Knowing which is which is how you read past the spin.
Why it matters beyond headlines
This isn’t pedantry; it changes real decisions:
- Finance. “Our fee is only going up 2%” sounds trivial. If the fee was 2% and becomes 4%, that’s 2 percentage points — but double your cost.
- Polls. A candidate moving from 45% to 48% gained 3 points, not 3 percent — as a percent change it’s actually a ~6.7% rise. News outlets almost always mean points.
- Health and risk. “Cuts your risk by 50%” is meaningless without the base. Half of a 2% risk is a 1-point drop to 1%; half of a 40% risk is a 20-point drop. Same “50%,” wildly different stakes.
Percentages don’t cancel — they compound
Here’s the other classic: a value goes up 50%, then down 50%. Back to where it started? No.
| Step | Value |
|---|---|
| Start | 100 |
| +50% | 150 |
| −50% (of 150) | 75 |
You end at 75, down a quarter. Each percentage is taken from a different base — the second 50% is half of 150, not half of 100. This is why a stock that drops 50% needs a 100% gain to recover, not another 50%. When changes stack, run them one at a time; the Percentage Calculator does exactly this without the mental slips.
The formula you actually need
For a straight percent change, it’s always:
(new − old) ÷ old × 100
The single most common error is dividing by the new value. From 40 to 50 is (50 − 40) ÷ 40 = 25% up; but 50 to 40 is (40 − 50) ÷ 50 = 20% down. Different percentages for the same 10-unit gap, because the starting point changed. Drop the two numbers into the Percentage Calculator and it keeps the base straight for you.
A quick sanity habit
When any number is already a percentage — a rate, a poll share, a probability — pause and ask: points, or percent of the original? Say the words out loud. That one-second habit is the whole skill, and it’s the same care that makes splitting a bill or converting units come out right the first time. For the everyday version of this math, see how to split the bill.