Learn how to calculate discount percentage, sale price, and original price using 3 discount formulas. Covers stacked discounts, fake sales, and shopping tips.
Whether you're shopping during a Black Friday sale, applying a coupon code at checkout, or marking down products as a business owner, understanding how discounts are calculated saves you money and prevents costly mistakes. There are three discount problems you'll encounter, and each requires a different formula. This guide covers all three.
Every discount problem gives you two values and asks you to find the third:
Sale Price = Original Price × (1 − Discount% ÷ 100)
Example: A $200 jacket is 25% off.
Sale Price = $200 × (1 − 0.25) = $200 × 0.75 = $150
You save: $200 − $150 = $50
Discount% = ((Original Price − Sale Price) ÷ Original Price) × 100
Example: A TV originally priced at $800 is on sale for $560. What's the discount?
Discount% = (($800 − $560) ÷ $800) × 100 = ($240 ÷ $800) × 100 = 30% off
Original Price = Sale Price ÷ (1 − Discount% ÷ 100)
Example: Shoes are on sale for $75, tagged as 40% off. What was the original price?
Original Price = $75 ÷ (1 − 0.40) = $75 ÷ 0.60 = $125
This is the most commonly miscalculated formula. Many people incorrectly add 40% to $75 (getting $105), which is wrong. You must divide by (1 − discount rate), not multiply by (1 + discount rate).
You don't always need a calculator for common discount amounts:
The most common. A percentage is subtracted from the original price. Sale Price = Original × (1 − rate). A 20% discount on a $200 item saves $40.
A flat dollar amount is deducted. Sale Price = Original − Fixed Discount. A $50 coupon on a $200 item reduces the price to $150, which is only a 25% discount — not the same as 25% off.
"Buy one get one free" is effectively 50% off when buying two. "Buy one get one 50% off" means you pay 100% for the first and 50% for the second, so the effective discount on two items is 25%.
This is where most people get confused. When two percentage discounts apply sequentially, they are not additive — they're multiplicative.
Example: A $100 item with 20% off, then an additional 10% off.
Step 1: $100 × 0.80 = $80 (after 20% off)
Step 2: $80 × 0.90 = $72 (after additional 10% off)
Effective discount: ($100 − $72) ÷ $100 = 28%, not 30%
Formula for stacked discounts: Effective Discount = 1 − (1 − D1)(1 − D2)
= 1 − (0.80)(0.90) = 1 − 0.72 = 28% effective discount
Fictitious pricing is a documented retail practice where the "original" price is inflated before a sale to make the discount look larger than it is. This is illegal in many jurisdictions but still occurs.
Warning signs of a fake discount:
Protection: Always compare the sale price against other retailers, not just the marked-down original price. A 40% discount that still leaves the item more expensive than a competitor's regular price is not a good deal.
Business owners need to understand the difference between discount and markup, as they're calculated on different bases:
Discount is calculated on the selling price (customer's perspective):
Discount% = (Amount Saved ÷ Original Selling Price) × 100
Markup is calculated on the cost price (business perspective):
Markup% = (Profit ÷ Cost Price) × 100
A product that costs $60 and sells for $100 has a 40% markup — but only a 40% discount would bring it back to $60. If you offer 50% off, you sell it for $50, which is below your cost. This is why retailers must calculate discounts against selling price, not cost.
To find the minimum sale price that still covers cost:
Minimum Sale Price = Cost ÷ (1 − Target Margin%)
If cost is $60 and you need a 20% margin: $60 ÷ 0.80 = $75 minimum price
Sales tax is applied to the final discounted price, not the original price. If a $100 item is 25% off and has 8% sales tax:
Note: Coupons from the manufacturer are sometimes treated differently from store discounts — in some states, tax is applied to the pre-coupon price. This is known as the "coupon tax" and is most common in the US for manufacturer-issued coupons.
Store A: $180 bag, 30% off. Store B: Same bag, originally $220, 40% off.
A winter coat originally priced at $350 is marked down 20% in November, then gets an additional 35% off the sale price in January.
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