Double Discount Calculator (Stacked %)

Stacked discounts are not additive, they are sequential. The first 20% off a $100 item brings the price down to $80. The second 20% is then taken off the new $80, not the original $100, which is $16 off, leaving $64. Total savings are $36 on a $100 item, or 36% effective, not 40%. The shortcut: multiply the remaining-fraction of each discount. (1 - 0.20) x (1 - 0.20) = 0.80 x 0.80 = 0.64, which is 36% off. The calculator surfaces this gap as the "additive misconception" row so the difference between what shoppers expect and what they actually pay is right there in the result.

Sequential promotions let a store apply an extra discount to an already reduced price. For example, 30% off followed by another 20% leaves 0.70 x 0.80 = 0.56 of the original price, an effective discount of 44%, not 50%. The calculator compares that result with the additive interpretation.

Convert each discount to a remaining-fraction and multiply them. For 25% off plus 15% off plus 10% off, the remaining fractions are 0.75, 0.85, and 0.90. Multiply: 0.75 x 0.85 x 0.90 = 0.57375. So you pay about 57.4% of the original, which is 42.6% off. To recover the dollar discount, multiply by the price: 0.57375 x $100 = $57.38, savings of $42.62. The same trick works for any number of stacked discounts, in any order (multiplication is commutative, so the final price does not depend on which discount you apply first).

Most often during layered promotions. A typical Black Friday flow: a 40% storewide sale, plus a 15% member discount, plus a 10% coupon at checkout. Naive math reads that as 65% off, but the real cut is 1 - (0.60 x 0.85 x 0.90) = 1 - 0.459 = 0.541, or 54.1% off. Same pattern shows up with credit-card cashback layered on a sale, employee discounts stacked on a clearance price, or back-to-school promos combined with student status. Anytime a customer sees "extra X% off" applied to an "already Y% off" price, that is a sequential stack and the percentages do not add.

This calculator applies tax to the discounted subtotal. With a $100 item, 25% off, and an 8% tax rate, it calculates a $75 subtotal, $6 tax, and an $81 total. Actual taxable receipts vary by state and by discount type, especially for manufacturer coupons, so use the rule that applies to the transaction.