A percentage point is the plain difference between two percentages: if a rate goes from 5% to 10%, it rose by 5 percentage points. Percent change measures the same move relative to where it started, so that rise is also a 100% increase, and both statements are true at once.
Mixing the two up is one of the most common ways numbers get misread in news stories, polls, loan offers and health claims. Below are the two formulas, a set of worked examples computed in Python, basis points (the finance version), and a quick checklist for reading any "X% change" claim. If you need the basics of percentages first, start with how to calculate a percentage.
What is a percentage point?
A percentage point is the unit for the arithmetic difference between two percentages. If unemployment moves from 3.5% to 4.2%, it rose 0.7 percentage points. You'll also see it written as "points", "pts" or "pp". Percentage points only make sense when both numbers are already percentages, such as interest rates, tax rates, vote shares, approval ratings or probabilities.
Percent change, by contrast, works for anything: prices, populations, page views, or rates. It answers "how big is this change compared with the starting value?" The same 3.5% to 4.2% move is a 20% increase in the unemployment rate, because 0.7 is 20% of 3.5.
The two formulas side by side
- Percentage-point change = new rate − old rate. From 5% to 10%: 10 − 5 = 5 percentage points.
- Percent change = (new − old) ÷ old × 100. From 5% to 10%: (10 − 5) ÷ 5 × 100 = 100%.
The 5-point figure tells you the raw distance between the two numbers. The 100% figure tells you how large that distance is relative to where you started. Neither is more correct; they answer different questions. The "% increase / decrease" mode of the Percentage Calculator gives you the relative figure, and a simple subtraction gives you the points.
Worked examples
Every row below was computed with these three Python functions, so you can check any figure yourself:
def points(old, new): return new - old
def pct_change(old, new): return (new - old) / old * 100
def basis_points(old, new): return (new - old) * 100
pct_change(6.5, 7.0) # 7.692...
basis_points(6.5, 7.0) # 50.0| Change | Percentage points | Percent change | Basis points |
|---|---|---|---|
| 5% → 10% | +5 | +100% | +500 |
| 1% → 2% | +1 | +100% | +100 |
| 40% → 41% | +1 | +2.5% | +100 |
| 3.5% → 4.2% | +0.7 | +20% | +70 |
| 6.50% → 7.00% | +0.5 | +7.69% | +50 |
| 4.00% → 3.75% | −0.25 | −6.25% | −25 |
| 52% → 48% | −4 | −7.69% | −400 |
| 20% → 15% | −5 | −25% | −500 |
Two patterns stand out. First, the same 1-point move can be a 100% increase (1% to 2%) or a 2.5% increase (40% to 41%), depending only on the starting value. Second, when the starting rate is below 100%, the percent-change figure is always the bigger-sounding number, which is why it tends to appear in headlines.
Why the difference matters
The gap between the two framings grows as the starting number shrinks. A "rates doubled!" headline about something moving from 1% to 2% is accurate, yet misleading if readers assume "doubled" implies a big real-world shift. The reverse also happens: a poll that slips from 52% to 48% "lost 4 points", which sounds smaller than the equally true "fell 7.7%".
Ambiguous wording causes real confusion. If a 20% tax rate is "raised by 10%", that could mean 20% × 1.10 = 22% (a 10% relative increase, or 2 points), or 20% + 10 = 30% (10 percentage points, a 50% relative increase). The gap is 8 points. Writing "percentage points" for the second meaning removes the doubt.
Basis points: the finance version
Banks, bond markets and central banks often describe small rate moves in basis points. One basis point is one hundredth of a percentage point (0.01 points), so 100 basis points equal 1 percentage point and 25 basis points equal 0.25 points. A mortgage rate going from 6.50% to 7.00% is a 50-basis-point rise. That's clearer than "rates rose 0.5%", which could mean 0.5 points or a 0.5% relative increase.
- To convert points to basis points, multiply by 100: 0.7 points = 70 bp.
- To convert basis points to points, divide by 100: 25 bp = 0.25 points.
- Basis points are always absolute. Like percentage points, they never mean a relative change.
The up-then-down trap
Percent changes don't cancel out. If a $100 price goes up 50%, it becomes $150. If it then falls 50%, it becomes $75, not $100, because the second change is measured from the new, higher base. Smaller moves behave the same way: up 10% then down 10% leaves you at 99% of the start (1.10 × 0.90 = 0.99). To undo a 50% increase you need a 33.3% decrease, and to undo a 50% decrease you need a 100% increase. Percentage points don't have this problem: up 5 points then down 5 points is back where you started.
Relative vs absolute risk
Health and safety headlines use the same two framings. If a risk goes from 2 in 1,000 to 3 in 1,000, the relative increase is 50%, but the absolute increase is 0.1 percentage points, or 1 extra case per 1,000 people. Both numbers are true. Before deciding how worried to be, look for the absolute figures behind any relative claim.
How to tell which one you're looking at
- "X percentage points" or "X points" is always a direct subtraction, and it's the harder-to-misread framing.
- "X% increase" or "X% higher" is relative to the starting value. Check the starting number before assuming it means a big absolute change.
- A bare "X%" with no qualifier is the ambiguous case. Find the two original figures and calculate both versions yourself if the distinction matters.
A quick checklist
- Find the two original numbers, not just the reported change.
- Subtract them to get the percentage-point change.
- Divide that difference by the starting value and multiply by 100 to get the percent change.
- Ask which figure the source reported, and why.
The "% increase/decrease" mode gives you the relative change; subtract the two raw numbers for percentage points.
Percentage Calculator →Frequently asked questions
What is a percentage point?
A percentage point is the unit for the simple difference between two percentages. A rate that moves from 5% to 10% has risen by 5 percentage points, even though that is a 100% increase relative to the starting rate.
What is the difference between percent and percentage points?
Percentage points measure the absolute gap between two percentages, found by subtraction. Percent change measures that gap relative to the starting value. Going from 40% to 41% is 1 percentage point but only a 2.5% increase.
How do I calculate a percentage point change?
Subtract the old percentage from the new one. If a rate goes from 3.5% to 4.2%, the change is 4.2 - 3.5 = 0.7 percentage points. To get the percent change instead, divide 0.7 by 3.5 and multiply by 100, which gives 20%.
What is a basis point?
A basis point is one hundredth of a percentage point, or 0.01 points. A rate that rises from 6.50% to 7.00% has increased by 50 basis points, which is 0.5 percentage points.
Why do news reports use percentage points?
Because it avoids ambiguity. Saying a rate rose 0.5% could mean half a percentage point or a 0.5% relative increase. Saying it rose 0.5 percentage points can only mean the rate went up by that much, for example from 4.0% to 4.5%.
If something rises 10% and then falls 10%, is it back where it started?
No. The fall is measured from the new, higher value, so you end up at 99% of the original (1.10 × 0.90 = 0.99). A 100 dollar price would end at 99 dollars.