Stacked Discounts vs. a Single Discount: The Real Math
Why two stacked percentage discounts never add up to their sum, with worked examples showing the real combined discount at different sizes.
A store advertising "20% off, plus an extra 10% off" isn't offering 30% off — it just sounds like it is. Stacked percentage discounts compound sequentially, and the gap between the advertised sum and the real total grows as the discounts get bigger.
| Discount 1 | Discount 2 | Sum (looks like) | Real combined discount |
|---|---|---|---|
| 10% | 10% | 20% | 19% |
| 20% | 10% | 30% | 28% |
| 30% | 20% | 50% | 44% |
| 50% | 50% | 100% | 75% |
Why the gap grows
Each discount is a percentage of whatever's left, not of the original price. The bigger the first discount, the smaller the base the second discount has to work with — so a second discount on a heavily-marked-down item removes less in absolute dollars than the same percentage would on the full price. That's also why "50% off, plus an extra 50% off" is never free: it's 75% off, since the second half only applies to the half that's left.
The one exception: dollar-amount discounts
A flat dollar-amount coupon (like "$10 off") doesn't have this compounding problem — $10 off is $10 off regardless of what it's applied to. The compounding effect only happens when two or more percentage discounts are stacked together.
The Discount / Sale Price Calculator lets you mix percentage and dollar-amount discounts in any order and shows the real combined result.