Percentage Calculator
Calculate percentages, percentage change and ratios in one place.
Calculation
Formula
Examples
| Input | Result |
|---|---|
| What is 25% of 80? | (25 / 100) x 80 = 20 |
| What percent is 15 of 60? | (15 / 60) x 100 = 25% |
| Percentage change from 50 to 75 | (75 - 50) / 50 x 100 = +50% increase |
| Increase 40 by 20% | 40 x 1.20 = 48 |
About this calculator
A percentage is a way of expressing a number as a fraction of 100, where the word "percent" literally means "per hundred." Percentages let you compare quantities of different sizes on a common scale, which is why they appear everywhere from store discounts and bank interest to test scores and statistics. This Percentage Calculator handles the three problems people run into most: finding a percentage of a number, working out what percent one value is of another, and measuring the percentage change between two values.
The core math is simple once you see it. To find X percent of Y, you convert the percent to a decimal by dividing by 100 and then multiply: X% of Y = (X / 100) x Y. To find what percent one number is of another, you divide the part by the whole and multiply by 100: (part / whole) x 100. To find percentage change, you subtract the old value from the new value, divide by the old value, and multiply by 100; a positive answer is an increase and a negative answer is a decrease.
To use the calculator, pick the type of problem you have, then type your known numbers into the labeled fields. For "X% of Y" you enter the percentage and the base number. For "what percent is X of Y" you enter the part and the total. For percentage change you enter the original value and the new value. The result updates as you type, so you can experiment with different inputs immediately.
Reading the results is straightforward. A result for "percent of" is an absolute amount in the same units as your base number. A "what percent" result is a proportion, so 25 means one quarter. A percentage change of +50% means the value grew by half its original size, while -20% means it shrank by a fifth. Note that a 50% increase followed by a 50% decrease does not return you to the start, because each step is taken relative to a different base.
The most common mistake is mixing up the base for percentage change, since growing from 50 to 75 is a 50% increase but shrinking from 75 to 50 is only a 33% decrease. Another pitfall is stacking percentages additively when they should compound, such as two successive 10% raises producing a 21% total rather than 20%. When in doubt, write out the part and the whole explicitly before you calculate.
Frequently asked questions
Divide the part by the whole and multiply by 100. For example, 15 out of 60 is (15 / 60) x 100 = 25%. The smaller number goes on top and the total goes on the bottom.
Each percentage is applied to a different base. Starting at 100, a 50% increase gives 150, and a 50% decrease of 150 removes 75, leaving you at 75 rather than back at 100. The decrease is larger in absolute terms because it acts on the bigger number.
Percentage points measure the absolute gap between two percentages, while percent measures relative change. Moving from 10% to 12% is a rise of 2 percentage points but a 20% relative increase. They are not interchangeable.
To add X%, multiply by (1 + X/100); to remove X%, multiply by (1 - X/100). Adding 8% tax to $50 gives 50 x 1.08 = $54, and taking 20% off $50 gives 50 x 0.80 = $40.
If a number already includes a percentage, divide rather than multiply. If a total of $108 includes 8% tax, the pre-tax amount is 108 / 1.08 = $100. Subtracting 8% of $108 would give the wrong answer.
Yes. Percentages above 100 simply mean the value exceeds the whole it is compared to. Doubling a number is a 100% increase, and tripling it is a 200% increase.
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