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Maths explained

Percentage Points vs Percent Change: The Difference That Trips Everyone Up

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.

Infographic showing a rate moving from 4 percent to 5 percent, described three ways: plus 1 percentage point, plus 25 percent relative change, and plus 100 basis points
Three correct labels for the same move: percentage points, percent change, and basis points.

Table of Contents

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:

  1. How far did the number move on the scale? Answer in percentage points. (4 to 5 is 1 point.)
  2. 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.

A comparison showing the wrong description 'rates went up by 1 percent' in red, versus two correct descriptions 'up 1 percentage point' and 'the rate rose 25 percent' in green
Both green descriptions are correct. They just answer different questions about the same move.

Percentage Points: The Plain Gap

A percentage point is just the difference you get by subtracting one percentage from another.

Difference in percentage points = second % − first %

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:

Percent change = (new − old) ÷ old × 100

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.

1 basis point = 0.01 percentage points

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

A decision guide: when a percentage itself moves, subtract to get percentage points or basis points, or divide by the old value to get percent change
One question decides the right word every time: are you subtracting, or dividing by the start?
The tell: percent change always needs a starting value to divide by. Percentage points never do. If you can't picture what number sits on the bottom of the division, you're looking at a percentage point, not a percent change.

Common Mistakes to Avoid

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

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.