HourlyMath

How Discounts Stack: The Math Behind "Extra 20% Off Sale Prices"

Updated July 2026 · 4 minute read

"30% off, plus an extra 20% off at checkout!" — and your brain, being a reasonable brain, whispers 50% off. The register disagrees, and the register is right: stacked discounts don't add, they multiply, and the difference is money. Here's the one-step method that makes every stacked deal transparent before you're holding it in line.

Why they don't add

Each discount applies to the price as it stands, not the original. A $100 jacket: 30% off takes it to $70. The "extra 20%" now applies to $70, not $100 — taking off $14, not $20. Final price: $56, a 44% total discount. The second discount worked on a smaller base, so it delivered smaller dollars. That six-dollar gap between the advertised feeling (50%) and the arithmetic (44%) is precisely why retailers phrase promotions as stacks — "30% + 20%" reads bigger than "44%," and reading bigger is the job.

The keep-rate shortcut

Convert each discount into what you still pay — 30% off means pay 70% (0.70); 20% off means pay 80% (0.80) — and multiply: 0.70 × 0.80 = 0.56. Pay 56%, save 44%, done, any number of layers, and order never matters (0.80 × 0.70 is the same product). More landmarks worth carrying into a store: 25% + 20% → 0.75 × 0.80 = pay 60% (40% off, not 45%). 50% + 30% → 0.50 × 0.70 = pay 35% (65% off, not 80%). 20% + 20% → 0.64 (36% off, not 40%). The pattern to internalize: the stack always underdelivers its sum, and the bigger the discounts, the wider the gap.

Comparing deals across stores

The keep-rate turns dueling promotions into one number. "40% off everything" (pay 0.60) versus "30% off plus members' extra 15%" (0.70 × 0.85 = pay 0.595): the stacked deal wins by half a percent — nearly a coin flip, nothing like the "45% vs 40%" it advertises as. A flat "$25 off $100" against "20% + 10%" ($100 → pay $72): the coupon wins at exactly $100 but loses as the cart grows, since percentages scale and flat dollars don't. When a decision involves real money, thirty seconds with the discount calculator beats vibes — it stacks any combination and shows the true total percentage.

Tax, and the good news about it

Sales tax lands after discounts in virtually all US jurisdictions — you're taxed on what you actually pay. The $100 jacket at our stacked 44% off with 8% tax: $56 × 1.08 = $60.48. One wrinkle: percentage discounts also shrink the tax (smaller base), while "$10 off" coupons in some places are applied after tax depending on who funds the coupon — if a receipt ever looks odd, that's usually the mechanism.

The retail-psychology footnote

None of this math is hidden — it's just unperformed, and promotions are engineered for the unperformed state. "Was $200, now 30% off, extra 20% today only" deploys an anchor price, an additive illusion, and a deadline in one breath. The countermeasure is boring and total: ignore the theater, compute the keep-rate, compare the final price to what the item is worth to you. Retailers versus one multiplication — the multiplication wins every time. (The same price-vs-cost thinking, from the seller's side of the counter, is margin vs markup — worth reading if you're ever the one designing the sale.)