How to calculate a discount
Multiply the original price by the discount to get the saving, then subtract it; or multiply the price by (1 − discount) in one step.
To find the discount from two prices, divide the saving by the original price: a $60 item marked down to $45 is $15 ÷ $60 = 25% off.
Stacked discounts do not add up
Two discounts applied one after the other multiply: "30% off, then an extra 20%" is a 44% discount, not 50%, because the second one applies to the already reduced price.
| Discounts | Total discount | Price of a $100 item |
|---|---|---|
| 20% + 10% | 28% | $72.00 |
| 30% + 20% | 44% | $56.00 |
| 50% + 20% | 60% | $40.00 |
| 40% + 40% | 64% | $36.00 |
How much more you must sell after a discount
A discount comes straight out of profit per unit, so volume has to rise by more than the discount to keep gross profit level. The extra sales needed are discount ÷ (margin − discount), using the margin before the sale.[2]
| Margin | 10% off | 20% off | 25% off | 30% off |
|---|---|---|---|---|
| 30% | 50% | 200% | 500% | loss |
| 40% | 33% | 100% | 167% | 300% |
| 50% | 25% | 67% | 100% | 150% |
| 60% | 20% | 50% | 71% | 100% |
At a 40% margin, a 25% discount needs 167% more sales, which is why deep discounts on low-margin items rarely pay unless they bring in customers who buy other things. Test a markdown before you run it, and compare it with the price increase calculator, which works the same idea in reverse. The margin calculator shows the margin at any sale price.
Advertising a sale honestly
The FTC's Guides Against Deceptive Pricing say a "former price" used in a comparison should be the actual, bona fide price at which the item was offered to the public in good faith for a reasonable period, not an inflated price set up only to make the discount look larger.[1] The same guides cover "buy one, get one free" and comparisons with other sellers' prices. State laws can add their own rules. If you sell on a marketplace, remember that its percentage fee is charged on the discounted price; the selling price calculator and the profit margin calculator show what is left.
Frequently asked questions
How do I calculate a percentage off?
Multiply the price by the percentage and subtract: 25% off $80 is $80 − $20 = $60.
How do I find the discount percentage from two prices?
Divide the difference by the original price: ($60 − $45) ÷ $60 = 25%.
Is 20% off then 10% off the same as 30% off?
No. It is 28% off, because the 10% applies to the price after the first discount: 0.80 × 0.90 = 0.72.
How does a discount affect profit margin?
The whole discount comes out of profit. A $44 item sold at $80 keeps $36; at 25% off it keeps $16, a margin of 27% instead of 45%.
How much more do I need to sell to make a discount worthwhile?
Divide the old profit per unit by the new profit per unit and subtract one. If profit per unit halves, you need twice the units.