Percentage Points Are Not Percent

If an interest rate moves from 2% to 3%, it has risen by one percentage point and by fifty percent. Both statements are correct, they describe the same event, and they differ by a factor of fifty. Choosing between them is not pedantry — it is the difference between a headline that informs and one that misleads, and it is the single most common way percentages are reported wrongly.

The rule in one line

A percentage point is the plain difference between two percentages. A percent change is that difference measured against where you started.

from 2% to 3%

percentage points  =  3 - 2            =  1 point
percent change     = (3 - 2) / 2 × 100 =  50%

The gap between the two answers grows as the starting number shrinks. Moving from 1% to 2% is one percentage point and a doubling. Moving from 50% to 51% is also one percentage point, and barely a two percent change. The point value stays flat; the percent value depends entirely on the base.

Which one to use

Use percentage points when the quantity being measured is already a percentage: interest rates, unemployment, market share, tax rates, conversion rates, poll results. Use percent change when the quantity is a count or an amount: revenue, visitors, weight, price.

• Unemployment went from 4% to 5%: one percentage point, or a 25% rise.
• Market share went from 10% to 12%: two percentage points, or a 20% rise.
• Revenue went from £4m to £5m: a 25% rise. Percentage points do not apply.

When both readings are interesting, give both. "Support rose four points, from 8% to 12% — a 50% increase" is longer than either alone and cannot be misread, which is usually worth the extra words.

How this gets used to mislead

Because the two framings are both defensible, whoever reports the number can pick whichever serves them, and neither is a lie. A fee rising from 0.2% to 0.3% is a "0.1 point adjustment" if you are charging it and a "50% increase" if you are paying it. Small bases are where this is most exploitable, because a tiny absolute move produces a huge relative one.

The tell is a percentage that is described as changing by a percentage, with no base given. If a report says a rate "rose by 30%" and never says what it rose from, the sentence carries almost no information. Ask for the two raw figures; the arithmetic is trivial once you have them.

The reverse trick

It also runs the other way. A drop from 40% to 30% is ten percentage points and a 25% fall, and describing it as "a modest ten percent move" quietly borrows the smaller-sounding word for the larger-sounding framing. Whenever the unit is left off entirely, treat the number as unverified.

Basis points, for the very small numbers

Finance runs into this so constantly that it invented a unit to end the argument. A basis point is one hundredth of a percentage point, so a hundred basis points is one point. A rate moving from 2.25% to 2.50% moved twenty-five basis points, and the phrase is unambiguous in a way that "a quarter of a percent" is not.

The idea is worth borrowing outside finance. If you find yourself writing "half a percent" about something that is itself a percentage, you have hit exactly the ambiguity basis points exist to remove.

When you have the two numbers

Subtract for the point difference, or divide the difference by the starting value for the percent change. Do the second one with a calculator rather than in your head — the mistake people make is dividing by the ending value instead of the starting one, which produces a plausible number that is quietly wrong in a consistent direction.