Discount Calculator

The math behind a discount is straightforward once you have the right formula for the direction you're solving:

• Amount Saved = Original Price × (Discount % ÷ 100)
• Sale Price = Original Price − Amount Saved
• Original Price (working backward from a sale price) = Sale Price ÷ (1 − Discount % ÷ 100)

The reverse formula is useful whenever a tag only shows the discounted price and the percentage off, but not the original price — common on clearance racks or “20% off marked price” signs where you want to know what the item cost before the markdown.

Worked example — Find Sale Price: an item originally priced at 1200 is marked 20% off. Amount saved = 1200 × 0.20 = 240. Sale price = 1200 − 240 = 960.

Worked example — Find Original Price:you see an item tagged at 960 with “20% off” printed on the sign. Original price = 960 ÷ (1 − 0.20) = 960 ÷ 0.80 = 1200, and the amount saved is 1200 − 960 = 240 — matching the first example in reverse.

A common misconception — stacked discounts aren't additive. If a store offers 20% off and then an extra 10% off at checkout, the total discount is not 30%. Each discount applies to the price remaining after the previous one, so on a 100 item: 20% off brings it to 80, then 10% off that 80 brings it to 72 — a total discount of 28%, not 30%. Successive percentage discounts always compound to less than their simple sum, because each later discount is taken off a smaller base.