Enter an old number and a new one and the page tells you the percentage increase or decrease, with the steps. You can also raise or lower a number by a percent, or compare two rates to see the difference in percentage points.
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Your answer
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What to enter
- Percentage change
- Enter the old number first and the new number second. A bigger new number gives an increase and a smaller one gives a decrease.
- Increase or decrease by a percent
- Enter a starting number and a percent. The page shows the new number, and the multiplier that does it in one step.
- Percentage points
- Enter two rates. The page shows the gap in percentage points, and also the percent change in the rate itself.
Worked examples
An increase: a grade
Your mark went from 62 to 71. What is the percentage change?
- Find the change: 71 – 62 = 9.
- Divide by the old number: 9 ÷ 62 = 0.145161.
- Multiply by 100: 0.145161 × 100 = 14.516129%.
That is a 14.516129% increase. Going back from 71 to 62 would be a 12.676056% decrease, because the percent is taken from the new starting point.
A decrease: a price
A price dropped from 48 to 36.
- Find the change: 36 – 48 = -12.
- Divide by the old number: -12 ÷ 48 = -0.25.
- Multiply by 100: -0.25 × 100 = -25%.
That is a 25% decrease.
Raising a number by a percent
Raise 200 by 15%.
- Work out the percent of the number: 15% of 200 = 30.
- Add it on: 200 + 30 = 230.
- The same thing in one step: multiply by 1.15. 200 × 1.15 = 230.
Lowering 200 by 15% gives 170, which is multiplying by 0.85.
Why up 50% then down 50% does not get you back
Start with 100 and add 50%. You get 150. Now take 50% off that. You get 75, not 100, because the 50% is taken from 150. To get back to 100 from 150, you would need a 33.333333% decrease.
| Step | Number |
|---|---|
| Start | 100 |
| Add 50% | 150 |
| Take off 50% | 75 |
Percent or percentage point?
Percent and percentage point are different, and mixing them up is a common exam mistake. Say an interest rate rises from 4% to 5%.
- Subtract the rates: 5 – 4 = 1 percentage point.
- For the percent change in the rate, divide by the first rate: 1 ÷ 4 × 100 = 25%.
| How you say it | Answer |
|---|---|
| In percentage points | 1 percentage point |
| As a percent change in the rate | 25% |
Both are correct. A newspaper might say the rate rose by one point, and another might say it rose by a quarter. The first is the gap between the two percents, and the second is how big the gap is compared with where it started.
How the percentage change is calculated
- Subtract the old number from the new number to get the change.
- Divide the change by the old number.
- Multiply by 100 to turn it into a percent. A positive answer is an increase and a negative one is a decrease.
- For percentage points, subtract one rate from the other and do not divide.
Percentage change = (new – old) ÷ old × 100
Assumptions to keep in mind
- The percent is worked out from the old number, so going from 50 to 60 is a 20% increase, while going from 60 to 50 is a 16.67% decrease.
- If the old number is negative, the page divides by its size without the minus sign. Textbooks handle this differently, so check your course.
- A change from 0 has no percentage, because you cannot divide by 0. The page asks you to use the plain difference instead.
- This page does the arithmetic only. It does not know whether a change is good or bad.
Mistakes that give the wrong answer
Swapping old and new
The same two numbers give different percents depending on which is the starting point. 50 to 60 is +20%, and 60 to 50 is -16.67%.
Treating up 50% then down 50% as no change
The second percent is taken from a bigger number. 100 up 50% is 150, and 150 down 50% is 75, not 100.
Mixing up percent and percentage points
A rate that goes from 4% to 5% is up 1 percentage point. It is a 25% increase in the rate itself. Both are true, so say which one you mean.
Using the new number as the base
Dividing by the new number gives the wrong answer. Divide the change by the starting number.
Adding percent changes together
A 10% rise followed by a 10% rise is a 21% rise, not 20%, because the second is taken from the new number.
Questions students ask
How do I calculate percentage change?
Subtract the old number from the new one, divide by the old number, then multiply by 100. For 62 to 71, that is (71 – 62) ÷ 62 × 100 = 14.52%. The first mode does it and shows the steps.
What is the difference between percent and percentage point?
A percentage point is a plain difference between two percents. If a pass rate goes from 60% to 66%, it is up 6 percentage points. It is also a 10% increase in the pass rate, because 6 is 10% of 60. The last mode shows both.
Why does a 50% rise followed by a 50% fall not get me back to the start?
Because each percent is taken from a different number. 100 up 50% is 150, and 50% of 150 is 75, so 150 down 50% is 75. You would need a 33.33% fall to get back to 100.
How do I increase a number by a percent in one step?
Multiply by 1 plus the percent as a decimal. To add 15%, multiply by 1.15. To take off 15%, multiply by 0.85. The increase and decrease modes show the multiplier.
Is percentage change the same as percentage difference?
No. Percentage change starts from an old number, so the order matters. Percentage difference compares two numbers with no starting point and uses their average. If you need to turn a plain percent of a number or a reverse percentage, the percentage calculator does that.
