How it works
"Percent" means "per hundred", so 20% is 20 out of every 100, or 0.20. Every percentage problem is a version of one relationship: part = percent × whole.
- X% of Y: divide X by 100 and multiply by Y. 20% of 150 = 0.20 × 150 = 30
- What percent is A of B: divide A by B and multiply by 100. 30 ÷ 150 × 100 = 20%
- Percent change: subtract the old value from the new one, divide by the old value, multiply by 100. A positive result is an increase, a negative one a decrease. (75 − 50) ÷ 50 × 100 = +50%
Worked example
A jacket was $80 and is now on sale for $60. What's the discount?
Percent change = (60 − 80) ÷ 80 × 100 = −25%. The price dropped 25%.
Going the other way, a 25% discount on $80 saves 0.25 × 80 = $20, leaving $60.
Frequently asked questions
How do I calculate a percentage of a number in my head?
Find 10% by moving the decimal one place left, then scale. 10% of 150 is 15, so 20% is 30 and 5% is 7.5.
Why isn't a 50% increase followed by a 50% decrease back to the start?
The second change is taken from a bigger number. 100 up 50% is 150, and 150 down 50% is 75. Percent changes compound; they don't cancel.
What is the difference between percent and percentage points?
If a rate goes from 4% to 5%, it rose 1 percentage point, but that's a 25% increase relative to the starting 4%.
How do I add a percentage to a price, like sales tax?
Multiply by 1 plus the rate. A $40 item with 8% tax costs 40 × 1.08 = $43.20.