How this is calculated
final price = price × (1 − discount %) × (1 − extra %); effective discount = 1 − the product
A single discount is straightforward: the sale price is the original times (1 − discount). The interesting case is the stacked discount — '25% off, plus an extra 20% off at checkout'. Intuition says 45% off; reality says 40%, because the second discount applies to the already-reduced price: 0.75 × 0.80 = 0.60 of the original. Retailers know the intuition and price the promotions accordingly.
The same multiplication explains why a discount and a price increase of the same percentage don't cancel. A price that rises 25% and then falls 25% lands at 93.75% of where it started — percentages are always relative to the current number, not the original.
The most defensive number here is 'effective total discount'. Compare it, not the advertised stack, against other offers — and against the item's normal price elsewhere. A '70% off' from an inflated anchor price routinely loses to a quiet 20% off an honest one.
Frequently asked questions
Why isn't 25% + 20% off equal to 45% off?
Because the second discount applies to the reduced price, not the original. The multipliers combine: 0.75 × 0.80 = 0.60, i.e. 40% total. The bigger the stack, the bigger the gap from the naive sum.
Is a bigger discount always the better deal?
Only against an honest reference price. Retail anchoring — inflating the 'original' before the sale — is common enough that price-history tools exist for exactly this reason. The effective final price is the only number that buys anything.
How do I calculate the discount from two prices?
Divide the reduction by the original: (original − sale) ÷ original × 100. A $80 item selling at $60 is 25% off.