Percentage Point Calculator
Work out the change in percentage points between two rates, the relative percent change and the move in basis points. Every answer shows the steps. It runs in your browser, so nothing you enter is stored.
Enter the rates
Result
Quick answer
A percentage point is the plain difference between two percentages. To find it, subtract the old rate from the new rate. A rate that moves from 4% to 6% has risen by 2 percentage points. In relative terms the same move is a 50% increase, because 2 is half of 4. Both statements are true, but they answer different questions, and mixing them up is one of the most common mistakes in news stories, reports and school work.
This calculator gives you both numbers at once, plus the move in basis points. Use the first tab when you know the old and new rates. Use the second tab when you know a starting rate and a change in points and want the new rate.
Percent and percentage points compared
The table below shows the same rate changes written both ways. The percentage point column never depends on the starting value. The relative column does.
| From | To | Percentage points | Basis points | Relative change |
|---|---|---|---|---|
| 2% | 3% | +1 | +100 | +50% |
| 4% | 6% | +2 | +200 | +50% |
| 10% | 20% | +10 | +1,000 | +100% |
| 20% | 30% | +10 | +1,000 | +50% |
| 50% | 45% | -5 | -500 | -10% |
| 5.25% | 5.00% | -0.25 | -25 | -4.76% |
| 0.5% | 0.75% | +0.25 | +25 | +50% |
How to calculate it
There are only two formulas to remember.
- Percentage point change = new rate – old rate
- Relative percent change = (new rate – old rate) ÷ old rate × 100
- Basis points = percentage points × 100
To go the other way, add the points to the starting rate. A rate of 4.5% plus 0.75 points is 5.25%. Do not multiply the starting rate by the points. Points are added and subtracted, while percent changes are multiplied.
Worked examples
Example 1, an interest rate. A bank raises its rate from 4.5% to 5.25%. The change is 5.25 – 4.5 = 0.75 percentage points, which is 75 basis points. In relative terms it is 0.75 ÷ 4.5 × 100, about 16.67%.
Example 2, an election. A party had 38% of the vote last time and 41% this time. It gained 3 percentage points. It did not gain 3%. In relative terms its share grew by about 7.9%.
Example 3, a survey. Support for a plan drops from 62% to 55%. That is a fall of 7 percentage points and a relative fall of about 11.3%.
Example 4, a test pass rate. A class pass rate goes from 80% to 92%. That is 12 percentage points, or a 15% relative increase.
Basis points explained
Finance uses basis points so that small rate moves are easy to say. One basis point is one hundredth of a percentage point, or 0.01%. Central banks, lenders and bond traders quote changes this way because “a 25 basis point cut” cannot be confused with “a 25% cut”.
| Basis points | Percentage points |
|---|---|
| 1 bp | 0.01 |
| 10 bps | 0.10 |
| 25 bps | 0.25 |
| 50 bps | 0.50 |
| 100 bps | 1.00 |
| 250 bps | 2.50 |
Common mistakes
- Saying “rose by 2%” when the rate went from 4% to 6%. Say 2 percentage points, or 50%, and be clear which one you mean.
- Comparing a relative change with a point change as if they were the same thing.
- Dividing by the new rate instead of the old rate when working out the relative change.
- Forgetting that the relative change depends on the starting rate. The same 2 point rise is a 100% jump from 2%, but only a 10% rise from 20%.
- Entering 0.05 when you mean 5%. Type the rates as percentages, such as 5.
Frequently asked questions
What is a percentage point?
A percentage point is the simple difference between two percentages. If a rate goes from 4% to 6%, it rose by 2 percentage points. It is a subtraction, not a ratio.
What is the difference between percent and percentage points?
A percent change compares the size of the change with the starting value. A percentage point change is just the gap between the two rates. A rise from 4% to 6% is 2 percentage points, but it is a 50% increase in relative terms.
How do I calculate a percentage point change?
Subtract the old percentage from the new one. New rate minus old rate gives the change in percentage points. For 12% to 9%, the answer is 9 – 12 = -3 points.
How do I calculate the relative percent change between two rates?
Divide the percentage point change by the starting rate and multiply by 100. For 4% to 6%, that is 2 ÷ 4 × 100 = 50%.
How many basis points are in a percentage point?
One percentage point is 100 basis points. A move of 0.25 points is 25 basis points, and a move of 1.5 points is 150 basis points.
Can a percentage point change be negative?
Yes. A fall in the rate gives a negative change. When you write it in words, say “fell by 3 percentage points” rather than “fell by negative 3”.
Why do news reports mix up percent and percentage points?
The two sound alike, and the larger number often looks more dramatic. When a report says a rate “rose 50%”, check whether it means 50 percent of the old rate or 50 points. Look at the old and new rates to be sure.
What if the starting rate is 0?
The percentage point change still works. The relative change does not, because you cannot divide by 0. The calculator shows “Not defined” in that case.
Is a rise from 10% to 20% a 10% increase?
No. It is a 10 percentage point increase and a 100% relative increase, because the rate doubled.
What is the percentage point change when an interest rate goes from 5.25% to 5.00%?
5.00 – 5.25 = -0.25 points, which is 25 basis points lower. The relative change is -0.25 ÷ 5.25 × 100, about -4.76%.
About this calculator
Written by Umar Khan, PhD student in engineering at NTNU. The calculator runs in your browser and does not store what you type.
Written by Umar Khan. Last updated: November 3, 2026.
Results are for general information. Check important figures against your source.