Free calculators for every common percentage question, plus plain-English explanations of how the math actually works — so you're not just getting an answer, you understand it.
A percentage is a way of expressing a number as a fraction of 100. The word itself comes from the Latin per centum, meaning "per hundred." So when something is 40%, that's shorthand for "40 out of every 100" — the same value as the fraction 40/100, or the decimal 0.40.
Percentages exist because raw numbers alone often don't tell you much. If a store's sales went up by 500 units last month, is that a big deal? It depends entirely on how big the store was to begin with. Going from 1,000 units to 1,500 is a 50% increase — huge. Going from 100,000 to 100,500 is a 0.5% increase — barely noticeable. The percentage gives you the scale of the change, independent of the size of the numbers involved.
If 15 out of 60 students in a class scored an A, what percentage is that? Divide the part by the whole: 15 ÷ 60 = 0.25. Multiply by 100: 0.25 × 100 = 25% of the class scored an A.
Most percentage questions boil down to one of three shapes, depending on which piece of information you're missing.
To find X% of a number, turn the percentage into a decimal by dividing by 100, then multiply. For example, to find 20% of 150: divide 20 by 100 to get 0.20, then multiply by 150. 0.20 × 150 = 30.
Divide the part by the whole, then multiply by 100. To find what percent 30 is of 150: divide 30 by 150 to get 0.20, then multiply by 100. 30 is 20% of 150.
Subtract the starting value from the new value to find the difference, divide that by the starting value, then multiply by 100. Going from 80 to 100: (100 − 80) ÷ 80 × 100 = 25% increase. A negative result means a decrease instead.
Try any of these directly with the Percentage Calculator, which handles all three and shows the steps for whatever numbers you enter.
| What you want | Formula |
|---|---|
| X% of a number | (X ÷ 100) × number |
| What % A is of B | (A ÷ B) × 100 |
| Percentage change | ((new − old) ÷ old) × 100 |
| Percentage difference | (|A − B| ÷ average(A,B)) × 100 |
| Markup on cost | ((price − cost) ÷ cost) × 100 |
| Profit margin | ((price − cost) ÷ price) × 100 |
| Convert % to decimal | % ÷ 100 |
| Convert decimal to % | decimal × 100 |
Once you notice them, percentages are almost impossible to avoid — they show up any time something needs to be compared proportionally rather than in raw terms.
Twelve free calculators, each with a plain-English breakdown of the math behind your answer.
Calculate percentages, percentage change, and what percentage one number is of another.
Find the discount amount, final price, or original price from a sale percentage.
Calculate sales tax, total price, or pre-tax price from a tax rate.
Add or remove VAT and calculate net price, VAT amount, and gross price.
Find your commission payout, the rate you were paid, or the sales needed to hit a target.
See how your money grows over time, or work out the principal or time needed to reach a goal.
Find your new salary after a raise, the raise percentage you got, or your old salary before it.
Find your tip amount, your total with tip, or how to split the bill among a group.
Find your selling price, or see markup % and profit margin % side by side — they're not the same number.
Compares two numbers relative to their average — a different, symmetric measure from percentage change.
Estimate body fat percentage from a few tape measurements, using the U.S. Navy method.
Find your percentage lost or gained, your target weight for a goal, or your starting weight.
Quick answers to the questions people ask most about percentages in general.
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin "per centum," meaning "per hundred." Saying "40%" is the same as saying "40 out of every 100," or 0.40 as a decimal, or 40/100 as a fraction.
Subtract the original value from the new value to find the increase, divide that by the original value, then multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25% increase.
A percentage point is a simple, direct difference between two percentages. A percentage change measures that same gap relative to the starting value instead. Going from 20% to 25% is a 5 percentage point increase, but it's a 25% increase in relative terms, since 5 is 25% of the original 20.
For round numbers, break the percentage into easy pieces: 10% of a number is just that number divided by 10 (move the decimal point one place left). Once you have 10%, you can build other percentages from it — 5% is half of 10%, 20% is double 10%, and so on.
Percentages let you compare things of different sizes on the same scale. Saying "20 more people" means very little without context, but saying "20% more people" tells you the scale of the change relative to where you started, regardless of whether the original group was 100 people or 100,000.