1. One Change, Two Correct Answers: Subtract or Divide
The Bank of England is the UK's central bank. Its main interest rate is called Bank Rate. In December 2021 its Monetary Policy Committee voted to increase Bank Rate by 0.15 percentage points, to 0.25% [1]. That means it was 0.10% before.
There are two natural questions you can ask about the change.
- How far did the number move? Subtract: 0.25 − 0.10 = 0.15. That is a rise of 0.15 percentage points.
- How big is the move compared with where it started? Divide the change by the starting value: 0.15 ÷ 0.10 = 1.5. That is a rise of 150 percent, which means the rate ended at 2.5 times its starting value.
Neither answer is wrong. They answer different questions. A percentage point measures a gap between two percentages. A percent change measures the change as a share of the starting value.
2. What "Percentage Point" Means in Official Statistics
Statistics offices use a separate word to avoid confusion. The European Union's statistics office, Eurostat, explains it in its glossary: the term percentage point is used when comparing two different percentages, and its abbreviation is "pp." Its example is a rate that was 10% and rose to 12%, which is an increase of 2 percentage points [2].
The Bank of England's announcement uses the same wording, "0.15 percentage points" [1]. For a rate that is itself a percentage, the gap in percentage points is a clear way to report a change.
Notice what the phrase does. If someone says "the rate rose by 0.25 percent," you cannot tell whether they mean 0.10% to 0.35% (a gap of 0.25 points) or a quarter of the old value. Saying "points" removes that doubt.
3. A Sales Tax Example: 2 Points, 25 Percent, or Under 2 Percent
Here is an invented example, so you can check every step yourself. Suppose a sales tax goes from 8% to 10%. This is not a real law. It just makes the arithmetic easy.
- Gap: 10 − 8 = 2, so the tax rate rose by 2 percentage points.
- Compared with the old rate: 2 ÷ 8 = 0.25, so the tax rate rose by 25 percent. A headline writer could truthfully say "tax rate up 25%."
- Compared with what you pay: a $10.00 item would carry 80 cents of tax before and $1.00 after. The tax amount is up 25 percent. But the total you hand over goes from $10.80 to $11.00, a rise of about 1.85 percent.
Three honest numbers came from one change. The only thing that differed was the starting value each one was compared with. That is the heart of this topic: "percent" always needs an answer to "percent of what?"
4. Why a Tiny Starting Value Makes a Big Percent Change
Back to the Bank of England. The starting rate was only 0.10%, so even a small step of 0.15 points was large compared with it, and the percent change came out as 150. If a rate had started at 5.00%, the same 0.15-point step would be a 3 percent change.
The rule is simple: for the same gap in points, a smaller starting value means a larger percent change. A rate moving from 1% to 2% is a 1-point rise but also a doubling.
So a phrase like "interest rates jumped 150%" can be accurate and still leave the wrong impression about how much a family's loan payments might change. The points figure and the percent figure tell you different parts of the story, and it helps to see both.
5. Why People Mix Up the Two Phrases
The main reason is that both are written with the same symbol, %. "Rose 3%" might be a 3-point gap or a 3 percent relative change. Writers also often shorten "percentage points" to "points," or drop the word entirely, so the reader has to guess.
It gets trickier because the word "point" also appears in other places: game scores, store reward points, and so on. A good habit is to look for the "from A to B" pair. If you see both numbers, you can work out the gap and the relative change yourself.
6. Three Questions to Ask When You See a Percentage Change
- From what to what? If both the starting and ending numbers are given, you can recalculate everything.
- Is it a gap or a ratio? "Points" means a subtraction. "Percent," "times," or "doubled" means a comparison with the starting value.
- How big was the starting value? When it is small, even a tiny gap can produce a huge-sounding percent.
When you write about numbers, include the starting and ending values as well, for example: "from 8% to 10%, up 2 percentage points (a 25% relative increase)."
7. Try It Yourself With Numbers You Already Meet
Say your tablet's battery drops from 80% to 60%. The gap is 20 percentage points. Compared with the 80% you started with, the battery lost 25 percent of its charge. Same change, two correct sizes.
Try a few more on paper, such as 30% to 33% (3 points, but a 10 percent relative rise). Then look for percentages in a news story or an advertisement, and ask whether the writer means a gap or a ratio. For real examples, the Bank of England publishes each rate decision on its website.