The short answer
A percentage-point change is the plain subtraction of two percentages: 4% to 5% is a rise of 1 percentage point. A percentage change is that move expressed relative to where you started: 4% to 5% is a 25% increase, because 1 is a quarter of 4.
Both statements describe the same event. They are not interchangeable, and only one of them is a ratio.
The confusion only arises when the quantity you are measuring is itself a percentage — an interest rate, a tax rate, a conversion rate, a share of the vote, a margin. For a quantity measured in units, such as 40 orders rising to 46, nobody is tempted to say "6 percentage points"; they say six more orders, or a 15% increase.
How each one is worked out
Write the starting figure as old and the finishing figure as new.
- Decide which figure is the baseline. The baseline is the "before", the older measurement, or the thing you are comparing against.
- Subtract to get the percentage-point move. Keep the sign: negative means a fall.
- Divide that difference by the baseline and multiply by 100 to get the relative change.
- Say which one you mean. "Up 1 point" and "up 25%" are both correct for 4% to 5%; "up 1%" is wrong for it.
The second formula is the one the calculator on this site uses, and it is why the baseline must be greater than zero: dividing by zero has no answer, and dividing by a negative baseline flips the sign of the result in a way that reads as nonsense.
Worked examples
A mortgage rate moves from 4% to 5%
The percentage-point change is 5 − 4 = 1 point. The percentage change is (5 − 4) ÷ 4 × 100 = 25.00% increase. Which one matters depends on the question. Your monthly interest bill is driven by the rate itself, so the one-point move is what you plug into a repayment calculation. But a lender comparing its own cost of funds year on year is looking at a quarter more interest than before, and 25% is the honest description of that.
Survey support rises from 40% to 46%
Six percentage points. As a relative change, (46 − 40) ÷ 40 × 100 = 15.00% increase. A headline saying "support up 15%" is defensible but will be read by most people as "support is now 55%". A headline saying "support up 6%" is simply wrong. "Up 6 points" is unambiguous and is why polling reports use it.
A fee is cut from 2% to 1.5%
The cut is 0.5 of a percentage point. Relative to the old fee it is (1.5 − 2) ÷ 2 × 100 = 25.00% decrease. The same arithmetic shows how misleading small bases can be: a charge rising from 0.5% to 1% is only half a percentage point, but it is a 100% increase — you now pay twice as much.
Edge case: unemployment falls from 8% to 6%
Minus 2 percentage points, and (6 − 8) ÷ 8 × 100 = 25.00% decrease. Note that the same two-point move from 4% to 2% would be a 50% decrease, and from 20% to 18% only a 10% decrease. The point move is identical in all three cases; the relative change is not, because the baseline is not.
| Old | New | Point change | Percentage change |
|---|---|---|---|
| 4% | 5% | +1.0 | +25.00% |
| 0.5% | 1% | +0.5 | +100.00% |
| 12% | 15% | +3.0 | +25.00% |
| 96% | 98% | +2.0 | +2.08% |
| 8% | 6% | −2.0 | −25.00% |
| 2% | 1.5% | −0.5 | −25.00% |
The 96% to 98% row is worth staring at. Two percentage points is a large improvement when you are already near the ceiling — it halves the failure rate, from 4% to 2% — yet the relative change in the success rate is a modest 2.08%. Describing progress near 100% is often clearer if you measure the thing that is shrinking.
Going backwards, and stacking changes
To undo a relative change, multiply rather than add. A 25% increase on 4% gives 4 × 1.25 = 5%. A 25% decrease from 8% gives 8 × 0.75 = 6%.
Relative changes do not add up, which is where most real errors live. Two successive discounts of 20% and 10% leave you paying 0.80 × 0.90 = 0.72 of the original price, a 28% total discount, not 30%. A 50% rise followed by a 50% fall leaves 1.50 × 0.50 = 0.75 of the original, a 25% net loss, not break-even. Percentage-point changes, by contrast, do add: three quarters of +0.25, +0.25 and −0.50 points leave the rate exactly where it started.
Common mistakes
- Saying "percent" when you mean "points". This is the one that makes a 6-point poll move sound like a 15% surge, or the reverse.
- Choosing the wrong baseline. Going from 50 to 60 is a 20% increase; going from 60 back to 50 is a 16.67% decrease. The gap is the same; the denominator is not.
- Adding relative changes. Month-on-month figures of +10% and +10% make +21%, not +20%, because the second month builds on the first.
- Averaging percentages as if the groups were the same size. A 90% pass rate in a class of 10 and a 50% pass rate in a class of 90 is not a 70% average; it is (9 + 45) ÷ 100 = 54%.
- Starting from zero. Growth from 0 to anything has no finite percentage change. Report the absolute figures instead of writing "infinite growth".
- Reading a point move on a percentage change. If growth slowed from 5% to 3%, that is a two-point slowdown in the growth rate, not a 2% fall in the underlying quantity, which is still rising.
Check it yourself
Put any pair of figures into the percentage change calculator. For 4 and 5 it prints 25.00% increase and shows the arithmetic as (5 − 4) ÷ 4 × 100 = 25.00%. For 8 and 6 it prints 25.00% decrease. Results are rounded to two decimal places, and the direction word comes from the sign, so an unchanged pair prints 0.00% with no direction.
The calculator deliberately refuses a baseline of zero or below and says so rather than printing a misleading number. For the percentage-point figure there is nothing to calculate: subtract the two percentages in your head, or use the basic calculator. If you need a percentage of a value rather than a change between two values, the percentage tool is the right one.
Related tools and guides
Reviewed October 1, 2026. Calculation methods and corrections.