A headline says "the interest rate rose from 4% to 5%." Ask how big that increase was and you'll get two different, both technically correct, answers: it rose by one percentage point, or it rose by 25%. Mixing those two up is one of the more common ways financial numbers get misread, and it's an easy mistake to make because both phrasings use the word "percent."
The two ways to measure a change
A percentage point is a simple difference between two percentages: 5% minus 4% is 1 percentage point, full stop. A percent change (or relative change) measures that same difference against the starting value: a move from 4% to 5% is a change of 1 point, but relative to the original 4%, that's a 25% increase (1 divided by 4). Both describe the identical move from 4% to 5% -- they just answer different questions. One tells you the absolute gap; the other tells you how large that gap is relative to where you started.
Why the gap between them grows at low starting values
The smaller the starting percentage, the more dramatic the relative change looks for the same point move. Going from 2% to 3% is only 1 percentage point, but it's a 50% relative increase. Going from 40% to 41% is also 1 percentage point, but it's only a 2.5% relative increase. This is exactly why a story like "risk of X doubled" can be describing a move from 1% to 2% -- true as a percent change, but a very different picture than "risk of X rose by 50 percentage points" would suggest.
Where this actually bites you
Interest rates, tax rates, and inflation numbers are the classic offenders. A central bank raising rates "by 0.25%" almost always means 0.25 percentage points (a quarter-point hike), not a 0.25% relative increase in the rate -- but the wording alone doesn't disambiguate it, which is why financial reporting increasingly spells out "basis points" (100 basis points = 1 percentage point) specifically to avoid this exact confusion. Tax bracket comparisons have the same trap: going from a 20% bracket to a 30% bracket is a 10 percentage point increase, but your tax bill on the same income rose by 50%, not 10%.
Check which one you're looking at
When you see a rate change described only as "X%," it's worth pausing to work out whether that's the point difference or the relative change -- the two numbers can be far apart, and only one of them usually matches what's being implied. The Percentage Calculator handles both percentage differences and percentage increase/decrease, so you can plug in the before-and-after numbers and see both figures side by side instead of doing the arithmetic in your head under time pressure.