The discount formulas
- Sale price = original price × (1 − discount ÷ 100).
- Discount percentage = (original price − price paid) ÷ original price × 100.
- Stacked discounts: final price = original price × (1 − d1) × (1 − d2). Real total discount = 1 − (1 − d1) × (1 − d2).
- Extra sales needed to keep the same total gross profit = discount ÷ (gross margin − discount), the gross margin being the profit as a percentage of the selling price.
- Gross margin after the discount = (gross margin − discount) ÷ (1 − discount).
Discounts are usually calculated on the price before sales tax, which is then charged on the reduced price: the percentage off is the same whichever way you look at it. Your margin, on the other hand, is always worked out before tax.
Three discounts worked out
| Situation | Calculation | Result |
|---|---|---|
| $80 item, 25% off | 80 × 0.75 | $60, a $20 saving |
| $100 quote, 20% off, then a 10% loyalty discount | 100 × 0.80 × 0.90 | $72, a real discount of 28% |
| Was $49.90, now $34.93 | 14.97 ÷ 49.90 | 30% off |
The second case is common in B2B, where suppliers quote chain discounts such as "20/10": a trade discount on the list price, then a volume or loyalty discount. Calling it "30% off" would be wrong. And if the business runs a 50% gross margin, that 28% discount cuts its profit to $22 on a $72 sale, a margin of 30.6%.
Don't confuse these with a cash discount for early payment. Terms such as "2/10 net 30" mean the buyer can take 2% off the invoice if it pays within 10 days; otherwise, the full amount is due within 30 days.
What a discount really costs
A discount comes straight out of your margin. At a 50% gross margin, a $100 product earns $50; at 20% off, it earns $30. To make the same total gross profit, you need 20 ÷ (50 − 20) = 67% more volume. At 28% off, the volume you need climbs to 127% more. Once the discount reaches your gross margin, every sale is made at cost: no amount of volume can make up for it.
This is the minimum to check before running a promotion. It does not account for customers who would have bought at full price, nor for those who discover you through the offer and come back later: the first make the promotion more expensive, the second help pay for it. To get your exact gross margin, start from your cost and selling price in the margin calculator.
Frequently asked questions
How do you calculate a percentage discount?
Sale price = original price × (1 − discount ÷ 100). An $80 item at 25% off costs 80 × 0.75 = $60, a $20 saving. The amount of the discount is simply the original price × the discount ÷ 100.
How do I calculate the discount percentage between two prices?
Discount percentage = (original price − price paid) ÷ original price × 100. A product marked down from $49.90 to $34.93 is $14.97 cheaper, which is 14.97 ÷ 49.90 = 30% off. Always divide by the original price: dividing by the sale price would give 42.9%, a wrong and misleading figure.
Do two discounts add up?
No, they multiply. 20% off followed by an extra 10% off is not 30% off: the second discount applies to a price that is already reduced. The final price is 0.80 × 0.90 = 72% of the original, a total discount of 28%. On $100, the customer pays $72, not $70.
What "was" price can a store show next to a sale price?
In the US, the Federal Trade Commission's Guides Against Deceptive Pricing say a former price comparison is legitimate when the former price is the actual, bona fide price at which the item was openly offered to the public on a regular basis for a reasonably substantial period. Inflating a reference price just to advertise a bigger discount is deceptive. Many states have their own rules on top.