Percentage change vs percentage points
Why a rate moving from 5% to 6% is both one point and a 20% change, how to calculate each correctly, and where the two get confused.
When a central bank lifts its policy rate from 5% to 6%, two news reports can describe the same decision in ways that sound like a contradiction. One says the rate rose by one percentage point. Another says rates rose 20%. Both are accurate, and neither is misleading on its own — they are answering different questions. The first measures the move on the scale the rate already lives on. The second measures the move relative to where it started.
The distinction is not pedantry. It changes how headlines are read, how fees are compared, and how risk is communicated. It also explains why a “small” one-point change can be enormous for some quantities and trivial for others.
Percentage points: the difference on the percentage scale
A percentage point is simply one unit on a percentage scale. If a value is expressed as a percentage and it moves from 5% to 6%, that is a change of one percentage point. You find it by subtracting:
percentage-point change = new percentage − old percentage
Nothing is divided and nothing is compared to a base. The unit exists specifically because “5% rose by 1%” is ambiguous: it could mean the value became 6%, or that it became 5.05%. Saying “rose by one percentage point” removes the ambiguity. Basis points extend the same idea to smaller moves: one basis point is one hundredth of a percentage point, so 50 basis points is 0.5 of a percentage point.
Percentage change: the move relative to the starting value
Percentage change answers a different question: how big is the move compared with the number we started from? The formula is:
percentage change = (new value − old value) ÷ |old value| × 100
Take 50 changing to 65. The difference is 15, and 15 divided by the starting value 50 is 0.30, so the percentage change is 30%. Reverse it — 65 down to 50 — and the difference is still 15, but the base is now 65, so the change is 15 ÷ 65 = 23.08%. A rise of 15 and a fall of 15 are not mirror images in percentage terms, because the denominator moved with the values.
The denominator is written with absolute value bars because direction is carried separately by the sign of the numerator. The free percentage calculator follows this convention: entering 50 as the starting value and 65 as the ending value returns a 30% increase, while an ending value below the start returns a decrease. The calculator suppresses the result entirely when the starting value is zero, because dividing by zero has no meaningful percentage answer — a quantity that goes from nothing to something has no finite relative growth rate.
The 5% to 6% example, both ways
Now the headline case. A rate moves from 5% to 6%.
- Percentage points: 6 − 5 = 1 percentage point.
- Percentage change: (6 − 5) ÷ 5 × 100 = 1 ÷ 5 × 100 = 20%.
It is both a one-point move and a 20% move. The point figure describes the move on the rate’s own scale; the 20% figure describes it relative to the old rate. Economists often prefer the point figure for rates because it is stable and additive, while the percentage figure is useful when asking how much larger a burden has become.
Scale changes what looks dramatic. Going from 1% to 2% is one percentage point, but the rate has doubled — a 100% increase. Going from 50% to 51% is also one percentage point, but only a 2% increase. The same point move produces a wild relative change at low bases and a tiny one at high bases. A table makes the pattern clear.
| Change | Percentage points | Percentage change |
|---|---|---|
| 2% → 3% | +1.0 | +50% |
| 5% → 6% | +1.0 | +20% |
| 8% → 8.5% | +0.5 | +6.25% |
| 4.75% → 5.25% | +0.5 | +10.53% |
| 20% → 25% | +5.0 | +25% |
| 10% → 5% | −5.0 | −50% |
Every row is arithmetically equivalent; the columns simply answer the two questions. Notice the 8% → 8.5% and 4.75% → 5.25% rows: both are half a point, but the relative sizes differ by almost a factor of two because the bases differ.
Where the confusion does real damage
Interest rates and central banking
Rate decisions are the classic trap. If a policy rate goes from 4.75% to 5.25%, that is 50 basis points, or half a percentage point. Reporting it as “a 50% rate rise” would be wrong by two orders of magnitude; reporting it as “rates rose 10.53%” is mathematically right but unusual. The convention in finance is to quote the point change or the basis points, precisely because percentage changes on a rate can swing from trivial to huge as the base moves.
Polling and elections
A candidate at 45% who rises to 48% has gained three percentage points. Describing that as “a 3% gain” understates it; the relative gain is 3 ÷ 45 = 6.67%. In tight races the point figure is the meaningful one, because the total is fixed at 100% and every point is taken from someone else.
Fees and lending
An arrangement fee that rises from 1.5% of a loan to 2% has risen half a percentage point but 33.3% in relative terms. Whether the point or the relative figure is the honest framing depends on what the borrower cares about: the outright cost on the loan amount, or the increase in the cost of the fee itself. Usually both matter, and quoting only one can shade the comparison.
Health and risk communication
This is where the gap is most consequential. “A drug reduces the risk of an event by 50%” sounds dramatic. If the absolute risk falls from 2% to 1%, that is a relative reduction of 50% but an absolute reduction of just one percentage point. Both numbers are true. Reporting only the relative figure without the starting risk is a well-documented way to overstate benefit, which is why regulators and medical journals push for absolute risk and the number needed to treat to be stated alongside it.
The same event can be framed to sound large or small by choosing the denominator. An absolute risk reduction of one percentage point means that, on average, 100 people must be treated for one to avoid the event — a number needed to treat of 100. If the starting risk were 20% instead of 2%, the identical relative reduction of 50% would drop the risk to 10%, an absolute reduction of ten percentage points and a number needed to treat of just 10. The percentage change is the same; the practical benefit is ten times larger. That is why the starting value, not the headline percentage, is the figure that matters.
Markup and margin: the same denominator problem in retail
A closely related confusion appears when businesses set prices. Markup is calculated on cost; margin is calculated on selling price. Take a $50 cost and a 40% markup. The selling price is 50 × 1.40 = $70, and the profit is $20. The gross margin is not 40% — it is 20 ÷ 70 = 28.6%. The same $20 of profit is 40% of the cost but only 28.6% of the price, because the denominator changed. The markup calculator shows both figures at once for exactly this reason: a 40% markup yields only a 28.6% margin, and mixing the two up is a classic pricing error that quietly eats profit.
A rule for choosing the right measure
- If the quantity being compared is itself a percentage — a rate, a share, a probability, a tax rate — prefer percentage points for the change.
- If you are comparing the size of two quantities or measuring growth against a base, prefer percentage change.
- When the base is very small, treat relative changes with caution; a percentage change from a tiny starting value can look alarming while being practically minor.
- When you quote a relative change, state the starting value too. “Cut by 50%” is not the same claim as “cut from 2% to 1%”, even though the first follows from the second.
Frequently asked questions
What exactly is a basis point?
A basis point is one hundredth of a percentage point, or 0.01%. It exists so small rate moves can be stated as whole numbers: a move from 5.00% to 5.25% is 25 basis points, not “0.25%”. Financial markets use basis points almost exclusively because they eliminate the point-versus-change ambiguity and make moves additive.
If a price falls 50% and then rises 50%, is it back to where it started?
No. Starting at 100, a 50% fall takes it to 50. A 50% rise on 50 takes it to 75. It needs a 100% rise from 50 to get back to 100, because the second percentage is applied to a smaller base. This asymmetry is the same denominator effect behind everything above, and it is why recovery percentages are always larger than the drop that preceded them.
Why did the percentage calculator hide the result when I entered zero?
Percentage change divides by the starting value. If that value is zero, the division is undefined, so there is no valid percentage to show. A quantity that starts at zero and becomes positive has increased by an infinite relative amount, which is not a useful number; the correct statement is simply the absolute change.
Should a rate rise be called a percentage or a percentage point?
Both, ideally. Say “up one percentage point, from 5% to 6% — a 20% increase in the rate”. That pairs the scale change with its relative size and removes any chance of the reader imagining the wrong thing.