Percent Off Calculator

A percent-off discount lowers a price by a share of the original amount. To find the sale price, turn the percentage into a decimal, multiply it by the original price to get the savings, and subtract. A $60 jacket at 25% off saves 0.25 × $60 = $15, so you pay $45. A quicker route is to multiply by what you keep: 25% off means paying 75%, and 0.75 × $60 = $45.

Working backward is just as easy. If an item costs $45 after 25% off, its original price was $45 ÷ 0.75 = $60. And if a $60 item is on sale for $45, the discount is 1 − 45 ÷ 60 = 25%. Fill in the two values you know and leave the others blank to do any of these.

Formula

Final price = Original × (1 − p) × (1 − q)

p

percent off as a decimal

q

stackable additional discount as a decimal, or 0

Amount saved = Original − Final price. Two stacked discounts p and q add up to a total discount of 1 − (1 − p)(1 − q), which is less than p + q.

Stores often let a coupon or loyalty discount apply on top of a sale. These stackable discounts are applied one after the other, each to the already-reduced price, so they do not simply add up. Take a $150 pair of boots marked 30% off, plus a 20% coupon. The sale brings the price to $150 × 0.70 = $105. The coupon then takes 20% of $105, or $21, leaving $84. You saved $66, which is 44% of the original price, not the 50% you might expect from adding 30% and 20%.

The order of two percentage discounts does not matter: 20% then 30% gives the same $84. Order does matter when one discount is a flat dollar amount. A $20-off coupon applied before a 30% discount saves more than one applied after it, because the percentage is then taken from a smaller number in the second case.

A big percentage is only a good deal if the original price was fair. Retailers sometimes inflate a "compare at" price to make a discount look larger, so check what the item has actually sold for recently. Compare unit prices for groceries and household goods, and remember that sales tax is calculated on the discounted price in most US states, so the savings carry through to the tax as well. Finally, a discount on something you would not otherwise buy is not saving money; it is spending less than the sticker said.

Frequently asked questions