Stacked Discount Calculator
The real price after two discounts applied one after another.
Input sheet
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Stacked discounts almost never add up the way the signs suggest. "20% off, then an extra 10%" feels like 30% off, but each cut applies to an already-reduced price, so the real saving is smaller than the two percentages summed.
How it works
Each discount applies to the already-reduced price, so they multiply: 20% then 10% leaves 0.8 × 0.9 = 72% of the price.
Because the second discount is taken on what remains after the first, the discounts multiply rather than add. The order does not matter — 20% then 10% lands at the same final price as 10% then 20% — but the combined effect is always less than simply adding the percentages.
This is the same math behind "buy more, save more" tiers and coupon-on-sale-price promotions, which is why retailers can advertise large stacked percentages while protecting their margin.
Final price = Original price × (1 − First discount) × (1 − Second discount), and Effective discount % = (1 − Final ÷ Original) × 100.
Worked examples
$100 item with 20% off, then a further 10% off. → $72.00 final price — a 28.0% effective discount, saving $28.
$100 × 0.80 = $80 after the first cut, then $80 × 0.90 = $72. You saved $28, not the $30 the two percentages seem to promise.
A $250 jacket marked 30% off with an extra 15% coupon. → $148.75 final — a 40.5% effective discount.
$250 × 0.70 = $175, then $175 × 0.85 = $148.75, which is 40.5% off rather than the 45% the labels imply.
Tips & gotchas
- Two discounts of x% and y% give an effective discount of x + y − (x × y ÷ 100), always less than x + y.
- The order of stacked percentage discounts never changes the final price, so ignore which one is applied first.
- A flat dollar coupon does depend on order — apply it after percentage discounts to save more, before them to save less.
- When comparing offers, convert each to its effective discount before deciding which is the better deal.
FAQ
Why isn't 20% + 10% equal to 30% off?
The 10% is taken on the price after the 20% is already removed, so it acts on a smaller amount. Multiplying 0.80 by 0.90 leaves 72% of the price, which is 28% off.
Does the order of two percentage discounts matter?
No. Multiplication is commutative, so 20% then 10% gives exactly the same final price as 10% then 20%.
How do I beat the stack with a dollar coupon?
A fixed-dollar coupon removes the same amount regardless of price, so apply it last — after the percentage cuts have shrunk the price — to maximize its proportional impact.
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