How percentages work
A percentage is a number out of 100. When you see 15%, it means 15 out of every 100, which is 0.15 as a decimal. Every calculation on this page comes from that one idea.
Percent of a number
Divide the percentage by 100, then multiply by the number.
percentage ÷ 100 × number
Example: 15% of 200 is 15 ÷ 100 × 200 = 30.
What percent one number is of another
Divide the part by the whole, then multiply by 100.
part ÷ whole × 100
Example: 42 out of 60 is 42 ÷ 60 × 100 = 70%.
Percent change
Subtract the starting number from the new number, divide by the starting number, then multiply by 100. A positive answer is an increase. A negative answer is a decrease.
(new − old) ÷ old × 100
Example: going from 80 to 100 is (100 − 80) ÷ 80 × 100 = 25%.
Add or subtract a percentage
To add a percentage, multiply the number by 1 plus the percentage as a decimal. To subtract, use 1 minus the decimal.
number × (1 ± percentage ÷ 100)
Example: 80 with 20% taken off is 80 × 0.8 = 64. This is how discounts, sales tax and tips are worked out.
Quick ways to do it in your head
- 10%: move the decimal point one place left. 10% of 250 is 25.
- 1%: move it two places left. 1% of 250 is 2.5.
- 5%: take half of 10%. 5% of 250 is 12.5.
- 20%: double 10%. 20% of 250 is 50.
- 15% tip: add 10% and 5%. For a 40 bill, that is 4 + 2 = 6.
Common questions
How do I find 10% of a number?
Move the decimal point one place to the left. 10% of 250 is 25, and 10% of 36 is 3.6.
How do I turn a percentage into a decimal?
Divide it by 100. 35% becomes 0.35, and 5% becomes 0.05. To go back, multiply the decimal by 100.
Can a percentage be more than 100?
Yes. 150% of a number is one and a half times that number. A price that goes from 100 to 250 has increased by 150%.
What is the difference between percent and percentage points?
Percentage points are the plain gap between two percentages. If an interest rate goes from 4% to 6%, it rose by 2 percentage points, which is a 50% increase in the rate.