Why percentages matter
Percentages show a part of a whole as a fraction of 100. You see them in sales (25% off), tips (15–20%), interest rates, and statistics. A few basic ideas make them easy to use.
The main ideas: “X% of Y” means multiply Y by X/100. “X is what percent of Y?” means divide X by Y and multiply by 100. “Percent change” from old to new is ((new − old) / old) × 100.
Finding a percentage of a number
To find X% of a number, multiply the number by X/100. Example: 20% of 400 = 400 × 0.20 = 80. On a calculator you can enter 400 × 20 % if it has a percent key, or 400 × 0.2.
Real use: a 15% tip on a $60 bill is 60 × 0.15 = $9. Tax at 8% on a $50 item is 50 × 0.08 = $4.
- 15% of 200 = 30
- 8% of 1,500 = 120
- 100% of any number = the number itself
What percent is X of Y?
Divide X by Y, then multiply by 100. Example: 25 is what percent of 200? 25 ÷ 200 = 0.125, 0.125 × 100 = 12.5%. So 25 is 12.5% of 200.
Use this when you have a part and a total: exam score (e.g. 42/50 = 84%), or “how much of my budget did I spend?”
Percent change (increase or decrease)
Percent change = ((new value − old value) / old value) × 100. If the result is positive, it’s an increase; if negative, a decrease.
Example: price goes from $80 to $100. Change = (100 − 80) / 80 = 0.25 = 25% increase. Example: salary goes from $60,000 to $57,000. Change = (57,000 − 60,000) / 60,000 = −5% (a 5% decrease).
Discounts: percent off vs amount off
“30% off $80” means the discount is 30% of 80 = $24; you pay $56. “$20 off $80” means you pay $60. Same original price, different final price depending on whether the discount is a percent or a fixed amount.
When you see “up to X% off,” the actual discount may be lower on some items. Always run the numbers for the specific price you care about.
Tools to use
Use our Percentage Calculator for “X% of Y,” “what percent,” and percent change. Use the Discount Calculator for sale price and savings with either a percent or a fixed amount off. Both run in your browser and need no sign-up.