Math calculator
Percentage Calculator
Find a percentage of a number, work out what percent one number is of another, or calculate the percent increase or decrease between two values.
Result
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How to calculate percentages
A percentage is a fraction of 100. To find a percentage of a number, divide the percentage by 100 and multiply by the number. To find what percent one number is of another, divide the first by the second and multiply by 100.
Percentage formulas
Examples
What is 15% of 80?
25 is what percent of 200?
What is the percent change from 40 to 50?
Frequently asked questions
How do I calculate a percentage in my head?
Start with 10% by moving the decimal one place left, then scale. For example, 10% of 80 is 8, so 20% is 16 and 5% is 4. Combine these to reach most common percentages quickly.
What is the difference between percent change and percentage points?
Percent change is relative: going from 10% to 15% is a 50% increase. Percentage points are absolute: the same move is an increase of 5 percentage points.
How do I calculate a percentage decrease?
Use the percent change formula. If the result is negative, the change is a decrease. For example, going from 50 to 40 is ((40 − 50) ÷ 50) × 100 = −20%, a 20% decrease.
How do I add a percentage to a number?
Multiply the number by (1 + percentage ÷ 100). To add 8% to 250, multiply 250 × 1.08 = 270.
Three ways to use the calculator
The calculator has three modes, and each one answers a different everyday question. "What is X% of Y?" takes a percentage and a value and returns the part, which is what you need for tips, discounts, sales tax, and commission. "X is what % of Y?" takes a part and a whole and returns the percentage, which is how you turn a test score of 42 out of 50 into 84%. "Percent change" takes a starting value and an ending value and tells you how much the number grew or shrank in relative terms.
Every result is shown to at most four decimal places, followed by a plain-English sentence and the formula that produced it. In percent change mode the sign is handled for you: a positive result is reported as an increase and a negative one as a decrease. The change is measured against the absolute value of the starting number, so moving from −20 to −10 is reported as a 50% increase rather than a confusing negative figure.
Two inputs are rejected because the math is undefined: a whole of zero in the "X is what % of Y?" mode, and a starting value of zero in percent change mode. There is no meaningful percentage of nothing, so the result stays blank until you change the value.
Percentage formulas
Percent means "per hundred," so every formula either divides by 100 to turn a percentage into a decimal or multiplies by 100 to turn a decimal back into a percentage. To find 18% of 250, divide 18 by 100 to get 0.18, then multiply: 0.18 × 250 = 45.
To find what percent 36 is of 48, divide the part by the whole and scale up: 36 ÷ 48 = 0.75, and 0.75 × 100 = 75%. For percent change, subtract the old value from the new one before dividing. Going from 120 to 150 is (150 − 120) ÷ 120 × 100 = 30 ÷ 120 × 100 = 25%, a 25% increase. Going the other way, from 150 to 120, is (120 − 150) ÷ 150 × 100 = −20%, a 20% decrease. The two percentages differ because each is measured against its own starting point.
Percent change versus percentage points
Percent change is relative and percentage points are absolute, and mixing them up is the most common percentage mistake in news reports and financial writing. If an interest rate rises from 4% to 5%, it has gone up by 1 percentage point, but the percent change is (5 − 4) ÷ 4 × 100 = 25%. Both statements are true; they just answer different questions. Use percentage points when both numbers are already percentages and you want the plain difference, and use percent change when you want to know how large the move is compared with where it started.
A related trap is assuming that a rise and a fall of the same percentage cancel out. A price that rises 25% from $80 reaches $100, but a 25% drop from $100 lands at $75, not $80. To get back to the original value you would need a 20% drop, because the fall is measured against the larger number.
Reverse percentages and stacked discounts
Working backward from a final value is where mental arithmetic usually goes wrong. If a jacket costs $60 after a 25% discount, the original price is not $60 plus 25% ($75). The sale price is 75% of the original, so the original is 60 ÷ 0.75 = $80. In general, divide by (1 − discount ÷ 100) to undo a discount and divide by (1 + rate ÷ 100) to undo a markup or sales tax.
Stacked discounts do not simply add. A 20% coupon followed by an extra 10% off leaves you paying 0.80 × 0.90 = 0.72 of the list price, a 28% saving rather than 30%. To check a combined discount, run the first percentage through the calculator, then use that result as the "Of value" for the second.
Everyday percentage problems
These are the situations the three modes are built for:
- Tips and sales tax – 18% of a $46 restaurant bill is 0.18 × 46 = $8.28
- Grades and quiz scores – 17 correct out of 20 is (17 ÷ 20) × 100 = 85%
- Raises and price changes – a salary moving from $52,000 to $55,120 is a 6% increase
- Discounts – 30% off a $45 item saves $13.50 and leaves $31.50 to pay
- Statistics – 312 survey respondents out of 1,200 is 26% of the sample
- Weight and fitness goals – losing 9 lb from 180 lb is a 5% decrease
Frequently asked questions
How do you find 20% of 80?
Convert 20% to a decimal by dividing by 100, then multiply: 0.20 × 80 = 16. A quick mental shortcut is to take 10% of 80, which is 8, and double it.
How do I calculate what percent one number is of another?
Divide the part by the whole and multiply by 100. For example, 30 out of 120 is (30 ÷ 120) × 100 = 25%. The "X is what % of Y?" mode does this for you.
How do you calculate percent increase?
Subtract the original value from the new value, divide by the original value, and multiply by 100. Going from 200 to 250 is (250 − 200) ÷ 200 × 100 = 25% increase. If the result is negative, it is a percent decrease.
What is the difference between percent change and percentage points?
Percentage points are the simple difference between two percentages, while percent change compares that difference to the starting value. Going from 10% to 15% is a rise of 5 percentage points but a 50% increase.
How do I take a percentage off a price?
Multiply the price by (1 − discount ÷ 100). For 30% off $45, multiply 45 × 0.70 = $31.50. To find the amount saved instead, use the "What is X% of Y?" mode: 30% of 45 is $13.50.
Why is there no result when I enter zero?
Dividing by zero is undefined. In "X is what % of Y?" mode the "Out of" value cannot be zero, and in percent change mode the "From" value cannot be zero, because there is no starting amount to measure the change against.