Percent vs percentage points: a small wording difference that changes the number

When a rate rises from 2% to 3%, describe it as a rise of one percentage point. If you want to express how large the change is relative to the old rate, it is also a 50% increase. Giving the starting and ending rates makes either description easier to interpret.

This distinction matters when comparing interest rates, survey results, conversion rates or any other number that is already a percentage.

The two measures

Percentage points measure the absolute gap between two percentages. 3% − 2% = 1 percentage point. Plain subtraction.

Percent change measures the relative jump: (3 − 2) ÷ 2 = 50%. The change is expressed as a fraction of wherever you started.

The same point increase produces a larger relative change when the starting percentage is smaller:

From → to	Percentage points	Percent change
40% → 44%	+4 pp	+10%
10% → 14%	+4 pp	+40%
2% → 3%	+1 pp	+50%
0.1% → 0.2%	+0.1 pp	+100%

For example, a hypothetical risk that doubles from one in a thousand to two in a thousand rises from 0.1% to 0.2%. The relative increase is 100%, but the absolute increase is one extra case per thousand. Both numbers, alongside the study’s context and uncertainty, are needed to interpret it.

If the starting value is zero, relative percent change is undefined because the calculation divides by zero. From 0% to 2%, you can still report a rise of two percentage points.

Percentages aren’t symmetric

Related trap: a percentage change doesn’t undo itself. Down 50% then up 50% won’t get you home. €100 falls to €50, then climbs to €75.

The two percentages came off different bases. The fall was 50% of 100; the rise was 50% of 50.

After a 20% fall, a 25% rise is needed to return to the starting value. After a 50% fall, it takes a 100% rise; after a 90% fall, a 900% rise. Calculate each change from the value in place at that step.

Apply successive discounts to the remaining price

Two successive 10% increases don’t make 20%. They compound: 1.10 × 1.10 = 1.21, so 21%. Stack a 20% discount on a 30% discount and you don’t get 50% off, you get 1 − (0.80 × 0.70) = 44% off. On a €100 item, the price goes to €80 and then €56. This assumes the second discount applies to the already-reduced price; check the offer’s terms.

The same logic means a 10% raise after a 10% pay cut leaves you slightly below where you started (0.90 × 1.10 = 0.99). And 3% inflation a year for a decade isn’t 30%, it’s 1.03¹⁰ − 1 = 34.4%.

Markup isn’t margin

The business version of the same base confusion. Add 25% to your cost and that’s a 25% markup, but the profit is only 20% of the selling price, which makes it a 20% margin. Cost €80, sell for €100: the €20 profit is 25% of 80 and 20% of 100. One transaction, two honest percentages, two different bases.

The markup and margin calculator shows both measures. The €20 difference here is before any other expenses: it is not necessarily the business’s net profit.

Reverse percentages: the subtraction trap

“The price including 21% VAT is €121, so I take off 21%?” No. 121 × 0.79 = 95.59, and the right answer is €100.

Undoing a percentage increase means dividing by 1.21, not subtracting 21%, because the 21% was worked out on the smaller pre-tax base. The same error turns up in bookkeeping, discount reasoning and salary arithmetic alike, and it has its own article with the working spelled out.

A checklist for any percentage claim

1. Points or percent? If the thing that changed was itself a percentage, state the starting and ending values as well as the change.
2. Percent of what? Find the base. Two percentages with different bases need that context before you combine or compare them.
3. Sequential changes? Multiply the factors (1.10 × 0.90…). Never add the percentages.
4. Undoing an increase? Divide by (1 + rate). Never subtract.

The percentage calculator covers X% of Y, percent change and what percent A is of B, showing the formula for each. To reproduce the 2%-to-3% example, select percent change and enter 2 as the old value and 3 as the new one. It returns 50%; subtract the two rates separately to get the one-percentage-point difference.

Last reviewed 2 October 2026.