The three-step discount formula
Step one: convert the percent off to a decimal by dividing by 100. Step two: multiply by the original price to get the discount amount. Step three: subtract the discount amount from the original price for the sale price.
Walk through 30 percent off a 90 dollar jacket. Thirty divided by 100 is 0.30. Then 0.30 times 90 equals 27 dollars of savings. Finally, 90 minus 27 equals 63 dollars. You pay 63 dollars.
The faster way: multiply once
You can skip the subtraction. If the item is 30 percent off, you pay 70 percent of the price. Multiply the original price by 0.70 directly: 0.70 times 90 equals 63 dollars. Same answer, one step.
This shortcut is the fraction method in disguise. Twenty-five percent off means you pay three quarters: 0.75 times the price. Fifty percent off means you pay one half. Use whichever route feels quicker.
Worked examples
Example 1: 20 percent off a 120 dollar pair of shoes. Discount amount: 0.20 times 120 equals 24 dollars. Sale price: 120 minus 24 equals 96 dollars. Shortcut check: 0.80 times 120 equals 96 dollars.
Example 2: 10 percent off a 45 dollar book. Discount: 0.10 times 45 equals 4.50 dollars. You pay 45 minus 4.50, which is 40.50 dollars.
Example 3: 25 percent off a 160 dollar espresso machine. Discount: 0.25 times 160 equals 40 dollars. Sale price: 160 minus 40 equals 120 dollars. Fraction check: you pay three quarters, and 160 times 0.75 equals 120 dollars.
Example 4: 15 percent off a 2,400 dollar furniture set. Discount: 0.15 times 2,400 equals 360 dollars. Sale price: 2,400 minus 360 equals 2,040 dollars.
Stacked discounts: 20% off, then 10% off
Here is where shoppers get tripped up. A second discount applies to the already-discounted price, not the original. Take 20 percent off followed by an extra 10 percent off a 100 dollar item. The first discount brings the price to 80 dollars. The second takes 10 percent of 80, which is 8 dollars, leaving 72 dollars. That is a total savings of 28 percent, not 30 percent.
The general rule: multiply the keep rates. For two discounts of 20 and 10 percent, multiply 0.80 by 0.90 to get 0.72. You pay 72 percent of the original, so the effective discount is 28 percent. For the reverse direction, computing the percent change between an old and new price, see our guide on how to calculate percent increase and decrease.
Finding the original price from a sale price
Sometimes you see the sale price and want the original. Divide the sale price by the keep rate. If a coat is 25 percent off and the sale price is 90 dollars, the keep rate is 0.75, and 90 divided by 0.75 equals 120 dollars. The original price was 120 dollars.
Another one: a TV marked 40 percent off, ringing up at 480 dollars. Keep rate is 0.60. Then 480 divided by 0.60 equals 800 dollars original. You can verify: 40 percent of 800 is 320, and 800 minus 320 is 480.
Common discount mistakes
The most expensive mistake is adding discounts: 20 percent plus 10 percent is not 30 percent off. The second is rounding the discount amount up or down before subtracting, which compounds on big purchases. Round once, at the very end. And remember that sales tax applies to the sale price in most US states, so the discount formula tells you the pre-tax price; tax gets added at the register.