Why "50% Off, Then Extra 50% Off" Isn't 100% Off
At checkout, "50% off, plus an extra 30% off" feels like it should land somewhere close to 80% off. The total that actually shows up is smaller, and it's easy to wonder whether the code glitched or the original price was padded to make the stack look bigger than it is. Usually it's neither. Stack two 50%-off discounts and it's tempting to read that as free. It isn't. And the reason is a basic math mismatch that retail signage is built to exploit.
Discounts multiply the remaining price, not the original
Each successive discount applies to whatever price is left after the previous one, not to the original price all over again. Take 50% off $100 and you're left with $50; take another 50% off that $50, and you're left with $25. A 75% total discount, not 100%. The two 50%-off steps compound against a shrinking base, exactly the way compound interest compounds against a growing one, just running in the opposite direction.
The general formula behind any stack
For two discounts d1 and d2 (as decimals), the combined discount is 1 − (1−d1)(1−d2), not d1 + d2. A "50% off, plus an extra 40% off" clearance sign works out to 1 − (0.5 × 0.6) = 70% off total. A genuinely large discount, but noticeably smaller than the 90% a straightforward add-the-percentages reading would suggest.
Why retailers stack discounts this way on purpose
Advertising two separate, smaller-sounding percentages side by side reads as a bigger deal than stating the single combined percentage outright, even when the combined number is accurate and could just be shown directly. This is a well-documented pattern in retail pricing psychology. Multiple smaller numbers presented in sequence tend to be perceived as adding up to more than an equivalent single number, which is exactly the gap between the intuitive (additive) and actual (multiplicative) math.
That gap is worth naming directly, because it's easy to feel tricked once you notice it: the sign isn't lying, and the discount code isn't broken. 70% off is still a real, substantial discount. The signage is just arranged to make the intuitive (wrong) reading more tempting than the actual one, and knowing the multiplicative math is what closes that gap.
What to actually do at checkout
If the goal is checking whether a specific stacked deal is what it claims to be, apply each discount to the running price one at a time rather than adding the percentages: take the first percentage off, then take the second percentage off whatever's left. If the goal is comparing two different stores' stacked offers against each other, convert each stack into its single combined percentage using the formula above first. Comparing "50% + 30%" to "60% + 15%" directly is comparing the wrong numbers; comparing the two combined totals is the honest comparison. And if there's no calculator handy, the safe mental shortcut is to treat any headline stacked percentage as an upper bound, not a promise: the real total is always somewhat lower than the sum of the parts.
Work out a stacked discount or a single sale price with the discount calculator.