Two discounts do not add up
A jacket is −30 %, and your loyalty card gives another −10 %. That is not −40 %. The second discount is taken from the price that is already reduced:
100 × (1 − 0.30) = 70 70 × (1 − 0.10) = 63 ← real discount 37 %, not 40 %
The gap grows with the numbers. −50 % and another −50 % is −75 %, not free. Shops know this, which is why “extra 20 % off sale prices” sounds bigger than it is. The table below shows the real figure for common pairs.
Working backwards from the sale price
“Was 129, now 90” — but was it? To check, divide the sale price by (1 − discount). 90 / 0.70 = 128.57, so the 30 % claim holds. If the maths gives a different “original” than the tag, the reference price may have been inflated before the sale. In the EU the Price Indication Directive requires the “was” price to be the lowest price of the previous 30 days, so this check is worth doing on big-ticket items.
The seller’s side of the same number
A discount looks small on the price and large on the profit. If an item costs the shop 60 and sells for 100, a 20 % discount cuts the price by 20 but the profit by half — from 40 to 20. That is why “how many more units do I need to sell to make up for the discount” is the question every retailer should ask before a promotion; this article walks through it, and the margin calculator gives the figures.
Discount, multibuy, rebate and markdown are four different sums
A discount comes off the price you would otherwise pay, and the arithmetic is the one above.
A multibuy is a discount in disguise, and the disguise usually flatters it. “Buy three, get one free” means you pay for three and take four: 25 % off, not 33 %. “Three for two” means you pay two and take three: 33 % off. The two look alike on the shelf and differ by eight points.
A rebate arrives after the purchase — a code, a refund, a credit on the next order. The saving is real only if you collect it, and the share of people who never do is exactly why the seller prefers it to a discount at the till.
A markdown is a cut from a reference price rather than from what you were going to pay. That makes the reference price the whole question — and in the EU it is regulated, which is the next section.
The price a shop is allowed to strike through
Announce a price reduction in the EU and you must state the prior price, defined as the lowest one you applied during at least the 30 days before the reduction. That comes from Article 6a of the price indication directive, inserted by the 2019 “omnibus” directive, and it is why a shop cannot lift a price for a week and then discover a sale.
Two practical consequences. As a buyer, the struck-through number is not the seller’s wishful retail price: it is a claim about the last 30 days, and a claim you can challenge. As a seller, a short promotional price you ran last month becomes the reference for this month’s reduction — plan the calendar, not just the percentage.
Member states differ in the details, especially for progressively increasing reductions and for goods on the market under 30 days. What does not differ is the principle: the reference price is a fact about the past, not a decision about the present. What a discount costs the shop that gives it is a different arithmetic again — see what a discount really costs.
Two discounts in a row
What two stacked discounts actually add up to.
| First discount | + 10% | + 15% | + 20% | + 30% |
|---|---|---|---|---|
| 10% | 19% | 23.5% | 28% | 37% |
| 20% | 28% | 32% | 36% | 44% |
| 25% | 32.5% | 36.3% | 40% | 47.5% |
| 30% | 37% | 40.5% | 44% | 51% |
| 50% | 55% | 57.5% | 60% | 65% |
Frequently asked questions
Yes, if you wanted four. You pay for three out of four, which is 75 % of the price — a 25 % discount. If you only needed one, the offer is worth nothing.
For a consumer it makes no difference: a percentage off the gross price is the same amount as the same percentage off the net price plus VAT on the rest. Prices in EU shops are shown VAT-inclusive, so just use the price on the tag.
Take 10 % by moving the decimal point, then scale. 30 % of 85: 10 % is 8.50, three times that is 25.50, so the sale price is 59.50.
Slightly, if you want three. Three for two is 33 % off; “buy three, get one free” is 25 % off. The catch is the quantity: a multibuy only saves money on what you would have bought anyway.
In the EU, yes, whenever it announces a reduction — and the previous price must be the lowest one applied in at least the 30 days before. National rules vary in the details, including for goods sold for less than 30 days.