How to use this calculator
Pick the question you want to answer from the menu, and the calculator shows only the boxes you need:
- What is X% of Y? for tips, discounts, commissions and tax.
- X is what percent of Y? for test scores, budget shares and completion rates.
- What is the percentage change from X to Y? for price changes, growth and pay raises.
- What is Y increased or decreased by X%? for adding a markup or taking a percentage off.
- What is the percentage difference between X and Y? for comparing two values with no clear “before.”
The answer updates as you type. Underneath you’ll find the steps, written so you could repeat them with a pencil, plus a couple of related answers, such as what you’d need to get back to where you started.
The percentage formulas
“Percent” means “per hundred,” so 15% is 15/100, or 0.15. Every percentage question is a variation on one relationship: part = percent ÷ 100 × whole.
Rearranging it gives the other questions. To find the percent, divide the part by the whole and multiply by 100. Percentage change is the same idea, where the part is the change and the whole is the starting value:
Percentage difference divides the gap by the average of the two values instead of by one of them:
Worked examples
Percent of a number. What is 15% of 80? Write 15% as 0.15 and multiply: 0.15 × 80 = 12. The same method gives an 18% tip on a $65 bill: 0.18 × 65 = $11.70.
What percent. You scored 45 out of 60. Divide: 45 ÷ 60 = 0.75, then multiply by 100 to get 75%. As a fraction, 45/60 reduces to 3/4.
Percentage change. A price rises from $50 to $65. The change is 65 − 50 = 15, and 15 ÷ 50 = 0.3, so that’s a 30% increase. Going the other way, from $80 down to $60, is a 25% decrease.
Increase by a percent. Add 15% to 200: 15% of 200 is 30, and 200 + 30 = 230. The shortcut is to multiply by 1.15 in one step. To take 15% off instead, multiply by 0.85.
Percentage difference. Two quotes come in at 40 and 50. The gap is 10 and the average is 45, so they differ by 10 ÷ 45 ≈ 22.22%.
Why percentage changes don’t cancel out
A rise followed by a fall of the same percentage leaves you lower than you started, because the second percentage is taken from a bigger number. This table shows what it takes to get back to 100 after each change:
| Starting from 100 | New value | Change needed to return to 100 |
|---|---|---|
| Increase 10% | 110 | −9.09% |
| Increase 20% | 120 | −16.67% |
| Increase 25% | 125 | −20% |
| Increase 50% | 150 | −33.33% |
| Increase 100% | 200 | −50% |
| Decrease 10% | 90 | +11.11% |
| Decrease 20% | 80 | +25% |
| Decrease 25% | 75 | +33.33% |
| Decrease 50% | 50 | +100% |
That’s why an investment that falls 50% has to double to recover, and why a “25% off” sale followed by a 25% price rise doesn’t bring a price back to where it was. The calculator shows this “return trip” figure whenever you use the change or increase/decrease modes. For a focused tool that also reverses a change and compares percentage points with percent, use the percentage change calculator.
Common percentages as fractions and decimals
Many percentages are easier to work with as fractions. These conversions come straight from the “what percent” mode:
| Fraction | Decimal | Percent |
|---|---|---|
| 1/100 | 0.01 | 1% |
| 1/20 | 0.05 | 5% |
| 1/10 | 0.1 | 10% |
| 1/8 | 0.125 | 12.5% |
| 1/5 | 0.2 | 20% |
| 1/4 | 0.25 | 25% |
| 1/3 | 0.3333… | 33.33% |
| 1/2 | 0.5 | 50% |
| 2/3 | 0.6666… | 66.67% |
| 3/4 | 0.75 | 75% |
| 3/2 | 1.5 | 150% |
So 25% of 80 is a quarter of 80, or 20, and 6.25% of 1,200 is 75. For anything less tidy, our fraction calculator converts any fraction to a decimal and percent exactly.
Tips for getting percentages right
- Find the base first. Every percentage is “of” something. In percentage change, the base is always the old value, which is why a change from 50 to 65 (+30%) is not the reverse of 65 to 50 (−23.08%).
- Use 10% as a stepping stone. Moving the decimal point one place gives 10%. Halve it for 5% and add the two for 15%.
- Watch percent versus percentage points. A mortgage rate moving from 6% to 7% is up 1 percentage point, but up about 16.67% relative to where it started.
- Percentages over 100% are fine. 150% of 40 is 60, and a price that triples has risen 200%.
- Combine changes by multiplying. Two years of 10% growth is 1.1 × 1.1 = 1.21, a 21% total rise, not 20%. Our compound interest calculator applies this over many years.
To add sales tax to a price, use the increase mode or the dedicated sales tax calculator. For averaging several percentages, such as test scores, see the average calculator or, if the scores carry different weights, the grade calculator.
How the calculator handles rounding
Computers store decimals in binary, which is why some software reports 0.1 + 0.2 as 0.30000000000000004. This calculator multiplies before it divides where it can (so 7% of 100 is exactly 7), removes that floating-point noise before displaying anything, and shows answers to up to 4 decimal places (2 for percentages). When a figure in the steps has been rounded, it’s marked with ≈ rather than =, so you can always tell an exact answer from a rounded one.
Percentage change from zero isn’t defined, because any increase from nothing is infinitely large, so the calculator asks you to use percentage difference instead. For percentage difference, if either value is negative, it uses the average of their sizes (absolute values) so the result stays meaningful.
Frequently asked questions
How do I calculate a percentage of a number?
Divide the percentage by 100 to turn it into a decimal, then multiply by the number. For 15% of 80, that's 0.15 × 80 = 12. Multiplying first and dividing by 100 at the end (15 × 80 ÷ 100) gives the same answer and is often easier in your head.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. If you got 45 questions right out of 60, that's 45 ÷ 60 = 0.75, or 75%. The whole always goes on the bottom of the division.
What's the formula for percentage change?
Subtract the old value from the new value, divide by the old value, then multiply by 100. A price that rises from $50 to $65 changed by (65 − 50) ÷ 50 × 100 = 30%. A positive answer is an increase; a negative answer is a decrease.
Why doesn't a 20% drop undo a 20% rise?
Because each percentage is taken from a different starting number. 100 plus 20% is 120, but 20% of 120 is 24, so a 20% drop takes you to 96, not 100. To get from 120 back to 100 you need a decrease of about 16.67%.
What's the difference between percentage change and percentage difference?
Percentage change has a clear before and after, and divides by the starting value. Percentage difference compares two values on equal terms and divides by their average, so the answer is the same whichever value you list first. For 40 and 50, the change is +25% one way and −20% the other, but the difference is 22.22% both ways.
What's the difference between percent and percentage points?
Percentage points measure the gap between two percentages by subtraction; percent measures it relative to the starting value. A rate that goes from 4% to 5% rose by 1 percentage point, which is a 25% increase in the rate itself.
Updated November 2026. Results are estimates for educational purposes and depend on the inputs you provide.