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How a Discount Is Calculated

The sale price formula is: sale price = original price × (1 − discount ÷ 100). On an 80 item at 25% off: 80 × 0.75 = 60, a saving of 20. The reverse direction answers "what was the original price?": original price = sale price ÷ (1 − discount ÷ 100) — an item sold at 60 with "25% off" marked should have listed at 60 ÷ 0.75 = 80; if the crossed-out price on the tag is higher than that, the advertised discount is inflated.

The Mistake Almost Everyone Makes: Stacked Discounts Do Not Add

When a store advertises two discounts applied one after another — say 20% off, then an extra 10% at checkout — the intuitive answer "that is 30% off" is wrong, and by a meaningful amount. Each discount applies to the price left over from the previous one, not to the original price, so the two rates multiply, not add: on a 100 item, 20% off brings it to 80, then 10% off that 80 brings it to 72 — an actual total discount of 28%, not 30%. The general rule for any number of stacked percentage discounts d₁, d₂, d₃... is: total remaining fraction = (1 − d₁) × (1 − d₂) × (1 − d₃)..., and the true combined discount is always slightly less than the simple sum of the individual percentages — the gap grows as more discounts are stacked or as the percentages get larger.

This matters most at checkout, in "extra X% off already-reduced items" sales, and whenever a retailer combines a storewide sale with a coupon or loyalty discount: the two percentage labels look additive but the wallet impact is not. Running both numbers through the tool shows the real final price and the real total percentage saved, rather than trusting mental addition.

Reading Sale Tags Correctly

A "was 100, now 60" tag implies a 40% discount (1 − 60/100); checking that 100 × 0.60 = 60 confirms the math, but it does not confirm the "was" price was ever the genuine selling price rather than an inflated reference price set just before the sale — a separate, non-mathematical thing worth being skeptical of. The discount percentage and the amount saved in currency are two different numbers that both matter: a 50% discount on a 10 item saves 5, while a 10% discount on a 500 item saves 50 — the lower percentage can still be the bigger real saving.

A Related Trap: Percentage Points vs. Percent

"The discount increased from 20% to 30%" is a 10 percentage-point increase, but it is a 50% relative increase in the discount itself (10 ÷ 20). Retailers and shoppers sometimes talk past each other because of this — "half as much off" and "10 points less off" describe very different situations depending on the starting percentage. When comparing two discount changes, be clear about which of the two you mean, since they can differ by a wide margin especially at low starting percentages.