Discount Calculator

How it works

Sale price = price × (1 − d₁) × (1 − d₂) − coupon · Amount off: (price − amount) × (1 − d₂) · Buy X get Y: groups = ⌊items ÷ (X + Y)⌋, deal items = groups × Y · Discount % = (original − sale) ÷ original × 100 · Original = sale ÷ ((1 − d₁)(1 − d₂))

Each percentage discount multiplies the running price, so stacked discounts do not add: 25% off then an extra 10% off is 32.5% in total, not 35%, because the second discount applies to the already-reduced price. An amount-off discount is subtracted from each item, and a coupon comes off the order after the percentage discounts, which is how most stores apply them. A buy-X-get-Y deal is worked out in complete groups: with buy 2, get 1 free, every third item is free, so 5 items give one free item and 6 items give two. The reverse modes divide instead of multiplying: the discount rate is the saving divided by the original price, and the original price is the sale price divided by the share of the price you still pay. Sales tax, if you add it, is charged on the discounted price, as US sales tax rules require for store discounts.

Worked example

An $80 jacket at 25% off is 80 × 0.75 = $60. An extra 10% off clearance brings it to 60 × 0.90 = $54 — a 32.5% total discount, saving $26. With a $5 coupon on top, you pay $49 (38.75% off). At 7% sales tax the $54 price comes to $57.78. Buying 3 shirts at $20 on a buy 2, get 1 free deal costs $40, a 33.3% discount. Working backwards, a $54 sale price after 25% and 10% off means the original price was 54 ÷ 0.675 = $80, and a drop from $80 to $60 is (80 − 60) ÷ 80 = 25% off.

Frequently asked questions