Percentages are everywhere, from discounts and tips to exam scores and pay rises, and almost everyone has stopped and asked “wait, which number do I divide by?”
This percentage calculator covers the seven questions people ask most. Pick the one that matches yours, type two numbers, and it gives the answer along with the formula it used, so you can follow the working.
How to use the Percentage Calculator#
- Pick your question. There are seven, such as “What’s A% of B?” or “Percent change from A to B”.
- Enter A and B. Type the two numbers. Use a minus sign for negative numbers.
- Read the answer. You get the result, a sentence in words and the formula used.
The seven questions and their formulas#
| Question | Formula | Example |
|---|---|---|
| What is A% of B? | A ÷ 100 × B | 20% of 150 is 30 |
| A is what % of B? | A ÷ B × 100 | 30 is 20% of 150 |
| Percent change from A to B | (B − A) ÷ |A| × 100 | 80 to 100 is +25% |
| A is B% of what? | A ÷ (B ÷ 100) | 30 is 20% of 150 |
| Increase A by B% | A × (1 + B ÷ 100) | 200 up 15% is 230 |
| Decrease A by B% | A × (1 − B ÷ 100) | 200 down 15% is 170 |
| Percent difference | |A − B| ÷ average of A and B × 100 | 80 and 100 differ by 22.2% |
Percent change goes both ways, but not equally#
Going from 80 to 100 is a 25 percent increase. Going from 100 back to 80 is a 20 percent decrease. The gap between the two numbers is the same, 20, but the percentage is measured against a different starting point each time. Always divide by the number you started from.
This is also why a 50 percent rise followed by a 50 percent fall doesn’t bring you back. Take 100, add half to reach 150, then take half off to get 75. You’re down 25 percent overall.
Percent change versus percent difference#
Use percent change when there’s a “before” and an “after”, like a price last month and this month. Use percent difference when two numbers are equal partners, like the heights of two buildings, and neither is the starting point. It divides by the average of the two, so it gives the same answer in either order. For 80 and 100, that’s 20 ÷ 90, which is 22.2 percent.
Working backwards from a price#
The “A is B% of what number?” mode answers the question “what was the original?”. If a coat costs 120 after a 20 percent increase, the original is 120 ÷ 1.2 = 100, not 120 minus 20 percent, which would be 96. It’s the same trap that catches people removing tax. See the VAT calculator and the sales tax calculator for that exact use.
Stacked discounts and percentage points#
Two discounts don’t add up. Take 20 percent off 100 to get 80, then take 10 percent off that to get 72. The total discount is 28 percent, not 30.
And watch the words. If an interest rate rises from 4 percent to 5 percent, it has gone up by one percentage point, but it has risen by 25 percent. Both are true, and they mean different things.
The seven questions, with one example each#
| Question | Example | Answer |
|---|---|---|
| What percent is A of B? | 45 of 60 | 75% |
| Percent change from A to B | 80 to 100 | 25% increase |
| Find the whole when A is B% of it | 30 is 12% | 250 |
| Increase A by B% | 200 up 15% | 230 |
| Decrease A by B% | 200 down 15% | 170 |
| What is B% of A? | 18% of 350 | 63 |
| Percent difference between A and B | 40 and 60 | 40% |
Percent difference divides by the average of the two numbers, here 50, so 20 ÷ 50 = 40 percent. Percent change divides by the starting number, so from 40 to 60 it is 50 percent. The two answers differ, and picking the right one depends on whether one of the numbers is a baseline.
Checking your own working#
A quick test is to use round numbers. 18 percent of 350 should be a bit under 20 percent, which is 70, so 63 looks right. For a percent change, ask whether the sign makes sense: from 80 down to 60 must be a decrease. If you are working backwards from a total that includes a percentage, divide by 1 plus the rate, not subtract. For discounts, tax and other money cases, see the percent off calculator and the VAT calculator.
Frequently asked questions#
Divide the percentage by 100 and multiply by the number. 20 percent of 150 is 0.2 × 150 = 30.
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 100 that is (100 − 80) ÷ 80 × 100 = 25 percent.
Divide the final price by 1 plus or minus the percentage. After a 20 percent increase, divide by 1.2.
Percent change measures from a starting value. Percent difference compares two values with neither as the starting point, using their average as the base.
Percentage points are the plain gap between two percentages. Percent is the relative change. From 4 percent to 5 percent is 1 percentage point, or a 25 percent rise.
Divide the first number by the second and multiply by 100. For 45 out of 60, 45 ÷ 60 = 0.75, which is 75 percent. Choose the first option in the calculator and enter the two numbers.
Divide the part by the percentage as a decimal. If 30 is 12 percent of a number, the number is 30 ÷ 0.12 = 250. This is useful for working backwards from a discount or a tax-inclusive price.