How to calculate percentages: the three formulas you need
"Percent" means "out of 100". Almost every percentage question you'll meet is one of three types, and each has a simple formula.
1. What is X% of a number?
Multiply the number by the percentage, then divide by 100.
- 15% of $80 = 80 × 15 ÷ 100 = $12
- A 20% deposit on a $35,000 car = 35,000 × 20 ÷ 100 = $7,000
A mental shortcut: 10% is the number with the decimal point moved one place left. From there, 5% is half of 10%, 20% is double, and 15% is 10% plus 5%.
2. What percent is one number of another?
Divide the part by the whole, then multiply by 100.
- 45 out of 60 on a test = 45 ÷ 60 × 100 = 75%
- $300 of a $1,200 budget spent = 300 ÷ 1,200 × 100 = 25%
3. Percentage increase or decrease
Subtract the old value from the new value, divide by the old value, then multiply by 100. A positive answer is an increase; a negative answer is a decrease.
- Rent rises from $500 to $540 a week: (540 − 500) ÷ 500 × 100 = 8% increase
- A price drops from $80 to $60: (60 − 80) ÷ 80 × 100 = 25% decrease
Why up and back down isn't the same
A 50% fall followed by a 50% rise doesn't get you back to where you started. $100 falls 50% to $50, and a 50% rise on $50 only takes it to $75. Each percentage is calculated on a different starting value. To recover a 50% fall you need a 100% rise.
Percent vs percentage points
If an interest rate goes from 4% to 5%, it has risen by 1 percentage point, but by 25 percent (because 1 is a quarter of 4). News reports and loan offers mix these up all the time, and the difference can be large.
Adding or taking away a percentage
To add 10% to a number, multiply by 1.10. To take 10% off, multiply by 0.90. This is the quickest way to apply tax, discounts or price rises in one step.
Try it: the percentage calculator does this instantly, free and in your browser.