50% Off Plus an Extra 20% Is Not 70% Off — Here Is the Real Number

Stacked discounts never add up. Two discounts of 50% and 20% give you 60% off, not 70%. Here is the one-line trick to work out any combination in your head, and where the difference actually costs you money.

A jacket costs 100. It is marked 50% off, and today there is an extra 20% off sale items. That is not 70% off — you pay 40, which is 60% off. The second discount does not apply to the original price; it applies to the already-reduced price, so it is 20% of 50, not 20% of 100.

The trick: multiply what is left, not what is taken off

Instead of adding the discounts, multiply what remains after each one. A 50% discount leaves 0.5 of the price. A 20% discount leaves 0.8. Multiply them: 0.5 × 0.8 = 0.4, so you pay 40% of the original and the true discount is 60%. This works for any number of stacked discounts. Three discounts of 30%, 20% and 10% leave 0.7 × 0.8 × 0.9 = 0.504 — barely half off, not the 60% you would get by adding them. The more discounts you stack, the further the naive sum drifts from reality.

The order never matters

Multiplication is commutative, so applying 20% first and then 50% gives exactly the same final price as the other way round. If a shop tells you the order matters for the discounts themselves, that is not arithmetic — it is a policy about which promotions may be combined at all. The arithmetic is indifferent.

Where it does matter: tax, shipping and fixed-amount coupons

Order becomes genuinely important the moment something is not a percentage. A fixed 20-off coupon combined with a 50% sale is worth very different amounts depending on sequence: take 50% off 100 and then 20 off, and you pay 30; take 20 off 100 first and then 50%, and you pay 40. That is a ten-unit difference on a single item, which is why checkout systems are specific about the order they apply things. Tax behaves the same way — a percentage applied after a fixed discount lands on a smaller base. Free shipping thresholds are the trap that catches people most often: discounts are usually applied before the threshold is evaluated, so a coupon can quietly drop your order below the free-shipping line and cost you more than it saved.

Working backwards: what single discount equals the stack?

To convert a stack into the single equivalent discount, multiply the remainders and subtract from 1. For 50% and 20%: 1 − (0.5 × 0.8) = 0.6, so 60%. This is the number worth computing before you shop, because "50% + 20% extra" is designed to read as 70% at a glance. A useful sanity check: stacked percentage discounts can never reach 100%, no matter how many you combine, because you are always taking a fraction of something that remains.

Our discount calculator handles stacked percentages, fixed-amount coupons and tax in the right order, and shows the single equivalent discount so you can compare two offers directly. It runs entirely in your browser — nothing you type is sent anywhere.