Subtract for points; divide for per cent. 4% to 6% is 6 − 4 = 2 percentage points. As a relative change it is 2 ÷ 4 = 50%. Both are correct descriptions of the same move, and they are not interchangeable.
What a percentage point is
A percentage point is the unit you get when you subtract one percentage from another. It exists because the alternative is genuinely ambiguous.
Say a rate went from 4% to 6% and you write “it rose by 2%”. A reader can take that two ways: rose to 6%, or rose by 2% of 4% — to 4.08%. Both readings are grammatical.
“Rose by two percentage points” has one reading. That is the whole point of the term, and it is why statistical agencies require it rather than merely prefer it.
Points or per cent
The rule of thumb is short: comparing two percentages, use points. Comparing two amounts, use per cent.
Unemployment 5.2% to 4.8%: down 0.4 percentage points. Sales £100k to £120k: up 20 per cent. The first pair are already percentages, the second pair are amounts.
Both figures are legitimate for a rate change, and sometimes the relative one is the more informative — a drop from 0.2% to 0.1% is only a tenth of a point and it is a halving. When you use it, say so: “halved, from 0.2% to 0.1%” leaves nothing to guess.
How it is used to mislead
The two figures diverge most when the starting percentage is small, and that is exactly where the substitution does the most work.
A risk rising from 2% to 3% is one percentage point. It is also a 50% increase. The second is true, and printed alone it invites a reader to imagine something far larger than one extra case in a hundred.
Both numbers belong in the sentence. “Rose by one percentage point, from 2% to 3% — a 50% relative increase” is longer and leaves the reader nowhere to be misled.
The page flags it when the relative figure is at least twice the move in points, since that is the range where the swap changes the impression rather than the wording.
Where the distinction is mandatory
Central bank rates. A rate cut is always quoted in points or basis points. A “25% cut” to a 4% rate would be meaningless without saying which reading applies.
Official statistics. Unemployment, inflation and participation rates are reported in percentage points as a documented style rule, not a preference.
Polling. A candidate at 42% who moves to 45% has gained three points. Poll reporting uses points throughout, which is why the margin of error is quoted in points too.
Market share. Going from 10% to 12% is two points of share and a 20% relative gain, and boardrooms have been misled by the second where the first was meant.
Basis points
A basis point is one hundredth of a percentage point. 100 basis points is 1 percentage point.
Finance uses them because the moves it cares about are small and the ambiguity is expensive. A yield moving from 3.25% to 3.50% is 25 basis points, and nobody has to work out whether that meant relative or absolute.
Written “bps” and said “bips”. It is not a different idea — just a finer unit of the same one, invented for the same reason.
Starting from zero
A move from 0% to 5% is five percentage points. As a relative change it is undefined, not infinite.
The relative form divides by the starting figure, and dividing by zero has no answer. Reporting “an infinite increase” is not a stronger claim; it is not a claim at all.
This is one of the cases where points are the only honest option, and the page returns nothing for the relative figure rather than a symbol that looks like a number.
Sources and methodology
The distinction is a style requirement in official statistics, not just a preference; these are the references.
Method. Both figures come from the same exact rationals, so they cannot disagree with each other, and the relative change is refused rather than reported as infinite when the starting figure is zero. The page also computes the ratio between the two figures and names it when the relative change is at least twice the move in points — which is exactly the situation in which the two get swapped. That engine is verified on every change against 81 hand-written assertions, including that a move of the same number of points from a smaller base always produces a larger relative change, and that a change from zero returns no relative figure at all. The count and the per-case breakdown are published on the formula verification page.
Read the guide
For a change between two ordinary amounts rather than two percentages, the Percentage Change Calculator is the one — there is no points reading there, only the relative one.