Suppose a central bank raises interest rates from 4% to 5%. Did rates go up by 1% or by 25%? Here's the catch: one of those is wrong, and the other is right, but not for the reason most people think. The rate went up by 1 percentage point, which is a 25% increase in the rate itself. This guide clears up the difference for good, with UK and US examples, five worked calculations, and the finance world's own shorthand, basis points, explained along the way.
Table of Contents
- The one-sentence answer
- Why "percent of a percent" is so confusing
- Percentage points: the plain gap
- Percent change: the relative move
- Quick comparison table
- Everyday examples where this bites
- It's not just a UK habit: US examples
- The finance shortcut: basis points
- Worked examples
- A quick way to never get it wrong
- Common mistakes
- Related calculators
- Frequently asked questions
- References
The One-Sentence Answer
A percentage point is the plain arithmetic gap between two percentages (5% minus 4% equals 1 point). A percent change is how big that gap is relative to where you started (1 divided by 4 equals 25%). They describe the same move in two different ways, and mixing them up changes the meaning entirely.
Keep the picture above in mind: one move, three correct labels. The rest of this guide is just applying that idea consistently.
Why "Percent of a Percent" Is So Confusing
The trouble is that the thing being measured, an interest rate, an inflation figure, a poll share, is itself already a percentage. So when it moves, there are two completely valid questions you could be answering:
- How far did the number move on the scale? Answer in percentage points. (4 to 5 is 1 point.)
- How big was that move compared to the starting value? Answer in percent change. (1 is a quarter of 4, so 25%.)
Both are true. The error is using the word for one while meaning the other. "Rates rose 1%" sounds like question 2 but gives the answer to question 1, so a listener imagines a tiny 1% relative nudge, when the rate actually jumped by a quarter.
Percentage Points: The Plain Gap
A percentage point is just the difference you get by subtracting one percentage from another.
- UK unemployment goes from 4.2% to 4.6%, a rise of 0.4 percentage points.
- A poll has a party at 38%, up from 35% last month, a change of 3 percentage points.
- A savings account pays 4.00%, cut to 3.75%, down 0.25 percentage points.
Notice you never divide here. Percentage points are the honest, unambiguous way to state a move between two percentages, which is exactly why statisticians and style guides insist on them. The UK's Office for National Statistics, in its official writing guidance, tells authors to use "percentage points" precisely to avoid this confusion.
Percent Change: The Relative Move
Percent change asks how large the move is in proportion to the starting figure. You use the same formula you'd use for any before-and-after comparison:
Take that 4% to 5% rate: (5 − 4) ÷ 4 × 100 = 1 ÷ 4 × 100 = 25%. The rate rose by a quarter of its former self. This is a genuine, correct statement, "the interest rate increased by 25%", and it's a very different message from "1 percentage point," even though both describe the identical move. If you want to check any relative move like this, the Percentage Increase Calculator and Percentage Decrease Calculator do it in one step.
Quick Comparison Table
Side by side, the three labels for the same underlying move look like this:
| Label | What it answers | How you calculate it | 4% → 5% example |
|---|---|---|---|
| Percentage point | The plain gap on the scale | Subtract: new % − old % | +1 point |
| Percent change | Size of the move versus the start | Divide: (new − old) ÷ old × 100 | +25% |
| Basis point | The plain gap, in finance-standard units | Multiply the point gap by 100 | +100 bps |
All three rows describe the exact same 4%-to-5% move. None of them is "more correct" than the others, they simply answer different questions, and the only mistake is answering one question while using the word for another.
The Everyday Examples Where This Bites
This isn't a maths-class curiosity, the confusion has real consequences.
Your mortgage. When the Bank of England moves its rate, a change from, say, 3.75% to 4.00% is only 0.25 percentage points, but on the rate itself that's a 6.7% increase, and on a tracker mortgage it flows straight to what you pay. Lenders and the media quote the point move; your wallet feels the relative one.
Inflation "falling" while prices rise. If inflation drops from 4% to 3%, that's down 1 percentage point, but prices are still rising, just more slowly. People routinely misread "inflation fell" as "prices fell." They didn't.
Poll numbers. A candidate going from 40% to 44% gained 4 percentage points. Report it as "a 10% surge in support" (4 divided by 40) and you've technically described the relative change, but most readers will picture a 10-point jump to 50%. This ambiguity is why serious pollsters always say "points."
Tax and interest rates. A basic tax rate rising from 20% to 22% is 2 percentage points, but a 10% increase in the rate. Framing changes how big it sounds, which is why you'll see both used, sometimes deliberately.
It's Not Just a UK Habit: US Examples
The confusion isn't unique to British newspapers. US financial media makes the identical mix-up with the Federal Reserve's target rate, unemployment reports, and inflation readings.
When the Fed moves its target range by "a quarter point," it means 25 basis points, 0.25 percentage points, the plain gap. If the target moves from 5.25% to 5.50%, that's a 0.25 percentage point rise, but a (5.50 − 5.25) ÷ 5.25 × 100 = 4.76% relative increase in the rate itself.
The US unemployment rate follows the same rule. When it moves from 3.7% to 4.3%, government reports describe that as a 0.6 percentage point rise, the official phrasing used by the Bureau of Labor Statistics. Financial commentary sometimes frames the identical move as "unemployment surged 16%" (0.6 ÷ 3.7 × 100 = 16.2%), which is also true, it's simply answering the other question.
The CPI headline works the same way. If annual inflation cools from 3.4% to 3.1%, that's a 0.3 percentage point decline. Prices are still rising by 3.1% a year, just 0.3 points slower than before, not falling. Whether you're reading the Bank of England, the Federal Reserve, or a national statistics office, the same one-sentence answer from the top of this guide applies without exception.
The Finance Shortcut: Basis Points
There's a third label you'll meet constantly in mortgage, savings, and investing news: the basis point (bps, pronounced "bips"). It exists purely to kill the ambiguity above.
So 100 basis points equal exactly 1 percentage point. When the Federal Reserve or Bank of England "cuts by 25 basis points," that's a 0.25 percentage-point cut, no confusion possible, because basis points can only mean the plain gap, never the relative change. That precision is exactly why finance adopted them. Our 4%-to-5% move is +1 percentage point = +100 basis points = +25% relative. Three labels, one move.
Worked Examples
Example 1: Central Bank Rate Hike
A central bank raises its policy rate from 4% to 5%. Percentage point gap: 5 − 4 = 1 pp. Percent change: (5 − 4) ÷ 4 × 100 = 25%. In basis points: 1 pp × 100 = 100 bps. All three describe the identical move.
Example 2: UK Unemployment
Unemployment rises from 4.2% to 4.6%. Percentage point gap: 4.6 − 4.2 = 0.4 pp. Percent change: (4.6 − 4.2) ÷ 4.2 × 100 = 9.52%. In basis points: 40 bps. A headline reading "unemployment jumped nearly 10%" and one reading "unemployment rose 0.4 points" describe the same reality very differently.
Example 3: Opinion Poll Swing
A party's polling share moves from 35% to 38%. Percentage point gap: 38 − 35 = 3 pp. Percent change: (38 − 35) ÷ 35 × 100 = 8.57%. In basis points: 300 bps. Most pollsters would report this as "up 3 points," which is the plain, unambiguous version.
Example 4: A Savings Rate Cut
A savings account's rate drops from 4.00% to 3.75%. Percentage point gap: 3.75 − 4.00 = −0.25 pp. Percent change: (3.75 − 4.00) ÷ 4.00 × 100 = −6.25%. In basis points: −25 bps. The point drop sounds tiny; the relative cut is over 6% less interest earned on the same balance.
Example 5: A Tax Rate Increase
A basic tax rate rises from 20% to 22%. Percentage point gap: 22 − 20 = 2 pp. Percent change: (22 − 20) ÷ 20 × 100 = 10%. In basis points: 200 bps. Here the two numbers happen to look closer together, 2 versus 10, but they still answer different questions and shouldn't be used interchangeably.
A Quick Way to Never Get It Wrong
- Moving between two percentages and want the plain gap? Subtract, and you get percentage points (or basis points).
- Want to know how big that move is versus the start? Divide by the old value, and you get percent change.
- Reading the news? If a percentage itself changed and someone says "by X%," pause, they may mean points. If they say "by X points" or "X basis points," it's the plain gap.
Common Mistakes to Avoid
- Saying "rose by X%" when you mean points. This is the single most common version of the error, and it silently swaps a plain gap for a relative one. Once you notice it, you'll spot it in headlines constantly.
- Assuming a small point move means a small relative move. A 1 point move on a base of 2% is a 50% relative change; the same 1 point move on a base of 50% is only 2%. The base rate matters as much as the size of the gap.
- Treating basis points as optional finance jargon. They exist specifically to remove the ambiguity above, ignoring them reintroduces the exact confusion they were built to solve, and misreading "25 bps" as 25 percentage points overstates a move by a factor of 100.
- Reading "inflation fell" as "prices fell." A falling inflation rate above zero still means prices are rising, only more slowly. Actual falling prices, deflation, is a much rarer and different event.
- Forgetting which number is the denominator. Percent change always divides by the older, starting value, not the newer one; dividing by the new value instead gives a different, incorrect percentage for the exact same move.
Related Calculators
- Percentage Calculator - find what percentage one number is of another, or the plain difference between two values
- Percentage Increase Calculator - calculate the relative percent increase between an old and new value
- Percentage Decrease Calculator - calculate the relative percent decrease, including reverse-calculating the original value
Frequently Asked Questions
What is the difference between a percentage point and a percent?
A percentage point is the simple arithmetic difference between two percentages (5% minus 4% equals 1 point). A percent (percent change) expresses that difference relative to the starting value (1 divided by 4 equals 25%). The same move is 1 percentage point and a 25% increase at the same time.
Is going from 4% to 5% a 1% increase or a 25% increase?
It's a rise of 1 percentage point, which equals a 25% relative increase in the rate. Calling it "a 1% increase" is incorrect, that phrasing describes relative change, and the relative change here is 25%.
What is a basis point?
A basis point is one-hundredth of a percentage point (0.01 pp). 100 basis points equal 1 percentage point. Finance uses them to state rate moves precisely, since they can only mean the plain gap, never a relative change.
Why do statisticians insist on "percentage points"?
Because saying a percentage "rose by X%" is ambiguous, it could mean the point gap or the relative change. "Percentage points" removes that ambiguity, which is why bodies like the UK's Office for National Statistics require it in official writing.
How do I calculate percent change between two percentages?
Use (new minus old) divided by old, times 100. From 4% to 5%: (5 minus 4) divided by 4, times 100, equals 25%. This tells you the size of the move relative to the starting figure.
Does this matter for my mortgage or savings?
Yes. A 0.25 percentage-point rate change sounds tiny, but relative to a low base it can be a several-percent change in the rate, and on a tracker mortgage or savings account it directly affects what you pay or earn.
Can inflation fall while prices rise?
Yes. Inflation dropping from 4% to 3% is a 1 percentage-point fall, but inflation above zero still means prices are rising, just more slowly. Falling inflation is not falling prices.
How do you convert basis points to a percentage point?
Divide the number of basis points by 100. For example, 250 basis points divided by 100 equals 2.5 percentage points. If you need the relative percent change instead, you also need the starting value, basis points alone don't tell you that.
Is a 2 percentage point rise the same size for every base rate?
No, and that's the whole point of the distinction. A 2 percentage point rise from 2% to 4% doubles the rate, a 100% relative increase. The same 2 percentage point rise from 20% to 22% is only a 10% relative increase. The point gap is identical; the percent change depends entirely on the starting value.
How do you calculate percentage points on a calculator?
Subtract the smaller percentage from the larger one, no special function needed: 5 minus 4 equals 1 percentage point. For the relative percent change, divide that difference by the original value and multiply by 100, which the Percentage Increase Calculator and Percentage Decrease Calculator do automatically.
Why do polls report the margin of error in percentage points?
Because a margin of error describes the plain range around a poll result, not a relative comparison. Saying "plus or minus 3 points" means the true figure could sit 3 percentage points above or below the reported number, a far more precise statement than "plus or minus 3 percent" would be.
References
- UK Office for National Statistics. Style guide: using percentages and percentage points correctly in official statistics. Guidance for writers on distinguishing the two terms in published releases.
- Bank of England. Monetary Policy Summary and explanatory notes on Bank Rate changes. Official record of Bank Rate decisions, stated in percentage points.
- Federal Reserve Board. Federal Open Market Committee statements on target rate changes, quoted in basis points. The FOMC's standard unit for describing target-rate moves.
- US Bureau of Labor Statistics. The Employment Situation news release. Monthly unemployment-rate changes reported in percentage points.
This article is for general education. Interest-rate and inflation figures are used as illustrative examples and change over time; check official sources such as your central bank for current rates.