The three percentage formulas
Almost every percentage question is one of three formulas. Percent of a number: number × percent ÷ 100. What percent one number is of another: part ÷ whole × 100. Percent change: (new − old) ÷ old × 100. The reverse question, "30 is 20% of what?", is just the first formula turned around: part ÷ percent × 100.
Percentages and your money
Discounts: 25% off an $80 jacket is $20 off, so you pay $60. If a store stacks an extra 10% off at the register, that's 10% of $60, not of $80, so the final price is $54, not $52.
Raises: a 3% raise on a $55,000 salary is $1,650 a year, or about $137 a month before taxes. Our Paycheck Calculator shows what that raise looks like after taxes.
Interest: a credit card at 24% APR charges about 2% a month. On a $3,000 balance, that's roughly $60 of interest in a single month. See how long it takes to clear with the Credit Card Payoff Calculator.
Tips: 20% of a $65 bill is $13. For splitting the check, the Tip Calculator does it all at once.
Mental math shortcuts
To find 10%, move the decimal one place left: 10% of 84 is 8.4. Halve that for 5% (4.2), double it for 20% (16.8), and add the two for 15% (12.6). For 1%, move the decimal two places: 1% of 84 is 0.84. Percentages also flip: 8% of 50 is the same as 50% of 8, which is 4.
Two common percentage mistakes
Percent vs. percentage points. If a mortgage rate rises from 6% to 7%, it went up 1 percentage point, but that's a 16.7% increase in the rate itself. News stories mix these up all the time.
Losses and gains aren't symmetric. If an investment drops 50%, from $100 to $50, a 50% gain only brings it back to $75. To get back to $100 it needs to double, a 100% gain. That's why big losses take so long to recover from.
Frequently asked questions
How do I calculate a percentage of a number?
Multiply the number by the percentage, then divide by 100. For example, 20% of 150 is 150 × 20 ÷ 100 = 30.
How do I find what percent one number is of another?
Divide the part by the whole, then multiply by 100. For example, 30 out of 150 is 30 ÷ 150 × 100 = 20%. This is how a test score of 42 out of 50 becomes 84%.
How do I calculate percent increase or decrease?
Subtract the old value from the new value, divide by the old value, then multiply by 100. Going from 80 to 100 is (100 − 80) ÷ 80 × 100 = a 25% increase. Going from 100 back to 80 is a 20% decrease, because the starting point changed.
How do I calculate a sale price after a discount?
Multiply the original price by (100 minus the discount) and divide by 100. A $80 item at 25% off costs 80 × 75 ÷ 100 = $60.
What's the difference between percent and percentage points?
Percentage points measure the plain difference between two percentages, while percent change measures the relative change. A rate going from 4% to 5% is up 1 percentage point, which is a 25% increase.
If something drops 50% and then rises 50%, is it back where it started?
No. A 50% drop takes $100 to $50, and a 50% rise from $50 only gets you to $75. Recovering from a 50% loss takes a 100% gain.