A grocery store discount labeled "buy one get one 50% off" and another labeled "25% off both items" sound like they might be roughly equivalent deals, and the honest answer is they're mathematically identical in that specific comparison — but stacked, sequential discounts in general are a genuinely common source of miscalculation, because the intuitive way most people combine percentages doesn't actually match how sequential discounts mathematically compound.
Why you can't just add two percentages together
The most common miscalculation: assuming a 20% discount followed by an additional 10% discount is equivalent to a single flat 30% discount. This feels intuitive, since 20 plus 10 does equal 30, but it's mathematically wrong, because the second discount is applied to the already-discounted price, not to the original price — meaning the second discount's actual dollar value is smaller than 10% of the original price, since it's 10% of an already-reduced number. A $100 item discounted 20% becomes $80; that $80 discounted a further 10% becomes $72 — a combined discount of 28% off the original price, not the 30% that simple addition would suggest.
The correct way to actually combine sequential percentage discounts
The mathematically correct approach multiplies the remaining-price fractions together rather than adding the discount percentages. A 20% discount leaves 80% of the original price remaining (expressed as a multiplier of 0.8); a further 10% discount leaves 90% of whatever remains (a multiplier of 0.9). Multiplying these remaining-price fractions together (0.8 times 0.9 equals 0.72) gives the actual final remaining price as a fraction of the original — 72% of the original price remains, meaning the true combined discount is 28%, matching the direct calculation above. This multiplicative approach, rather than simple addition, is the general rule for correctly combining any sequence of percentage-based discounts.
Why the order two discounts are applied in doesn't actually change the final result
A genuinely useful and slightly counterintuitive fact: for straightforward percentage-based discounts (as opposed to a flat fixed-dollar discount, covered separately below), the order in which two sequential percentage discounts are applied doesn't change the final price at all. Applying 20% off followed by 10% off produces the exact same final price as applying 10% off followed by 20% off, because multiplication is commutative — 0.8 times 0.9 equals exactly the same result as 0.9 times 0.8, regardless of which specific order the two multiplications happen in. This holds true for any number of sequential percentage discounts, not just two, which is a genuinely useful thing to know when a store applies multiple different percentage-based promotions to the same purchase in whatever order their system happens to process them.
Why mixing a percentage discount with a flat dollar discount does change based on order
The order-independence described above specifically applies to combining multiple percentage-based discounts with each other — it breaks down as soon as a flat, fixed-dollar discount (like "$10 off") gets mixed into the sequence alongside a percentage discount, because a fixed dollar amount doesn't scale proportionally with the current price the way a percentage does. Applying a $10 flat discount before a 20% percentage discount produces a genuinely different final price than applying that same 20% percentage discount first and the $10 flat discount second, since the percentage discount is calculating 20% of two different base amounts depending on which order the two discounts are actually applied in. If you're ever given a choice about which order a store will apply a mixed flat-and-percentage discount, doing the arithmetic for both orderings (rather than assuming they're equivalent, since same-type percentage discounts are order-independent but this mixed case genuinely isn't) can reveal a real, calculable dollar difference worth knowing about before checkout.
Why "buy one get one X% off" needs its own separate calculation
A "buy one get one 50% off" promotion applies the discount to only one of the two items, meaning the actual combined discount across the full two-item purchase is considerably smaller than the flat 50% figure that appears prominently in the promotion's name might casually suggest — the true combined discount across both items together works out to 25% of the total two-item price, not 50%, since only one of the two items in the pair actually receives that 50% reduction while the other is paid at full price.
Calculating your own stacked discounts
Our stacked discount calculator handles the correct multiplicative combination of sequential percentage discounts automatically, sidestepping the common simple-addition miscalculation described above and giving you the actual final price rather than an intuitive but mathematically incorrect estimate.