Discount Calculator

What is a discount

A discount is a reduction in the selling price, almost always expressed as a percentage of the price you started from. It is not a fixed amount and not a property of the product: it is a percentage applied to a number, and changing that number changes what the discount is worth. 30% off 80 is 24; the same 30% off 300 is 90.

The word covers two different things worth keeping apart. To the buyer a discount is a saving, measured in money not spent. To the seller it is margin given up, measured in profit lost. The same 10% on the tag is a tenth to the customer and often a quarter of the profit to the shop, and the two do not compare.

How to calculate a discount

The formula is one line: final price = original price × (1 − discount ÷ 100). 30% off 120 is 120 × 0.7 = 84. To get the percentage from two prices, do the reverse: the difference divided by the original price, times 100. From 120 to 84 is 36 ÷ 120 = 30%.

The three numbers are tied together, so any two give the third. That is why this one solves in all three directions rather than only forwards.

• What will I pay? original price and percentage in. €120 at 30% off is €84, saving €36.
• What percentage is this? original and final price in. From €120 down to €84 is 30% off: the number to compare one sale against another.
• What was it before? percentage and final price in. €84 after 30% off was €120. This is the one worth checking when a shop shows only the new price and the claim.
• What do two discounts come to? add a second percentage and the page shows both the final price and the real combined discount, which is always less than the two added together.

Discount, markdown, margin and list price: the difference

• List price the price before any discount, sometimes called RRP. The number a sale is measured against, and, in the EU, one that has to have been genuinely charged for a period before being used as a reference.
• Markdown against markup a markdown is a cut from the selling price; a markup is what is added to the cost to get there. A 50% markup is only a 33% margin.
• Margin profit as a share of the selling price. The number a discount eats directly.
• Net price what you actually pay after everything is applied. Worth checking whether it includes VAT, which is a separate calculation.
• Effective discount the single percentage equivalent to a chain of discounts. The only one worth comparing between shops.

Do two discounts add up?

A 20% discount followed by a further 10% is not 30% off. The first takes €20 off €100, leaving €80; the second takes 10% of €80, which is €8, not €10. You pay €72 and the real discount is 28%. The gap grows with the numbers: 50% then 50% is 75% off, not 100%, which is the clearest way to see that the two cannot simply be added.

This is also where "extra 20% off sale prices" gets its force as a sign. It sounds like it should be added to the sale discount and it never is, so the headline number a shopper carries in their head is always larger than what they get. Running the two through here takes ten seconds and gives the figure to compare against a competitor who quotes one number.

The same arithmetic in the other direction is how a price rise hides. A 20% cut followed by a 25% increase lands exactly back where it started, because the increase applies to the smaller base. Any claim of the form "reduced then restored" deserves the actual numbers.

What a discount costs the seller: discount against margin

For anyone selling rather than buying, the number that matters is not the discount but what it does to the margin, and the relationship is brutal. On a product with a 40% margin, a 10% discount does not cost a tenth of your profit: it costs a quarter of it, because the discount comes entirely out of the margin and not out of the cost.

The rule of thumb worth carrying: discount ÷ margin is the share of profit you have given away. Ten points off a forty-point margin is a quarter gone; twenty points off is half. And to earn the same total profit you now need to sell proportionally more, which is the calculation most "let us just discount it" conversations skip.

When the discount calculation looks wrong

• “Fill in two of the three fields” only one is filled. Two of the three define the third; one defines nothing.
• “Clear one field” all three are filled, so there is nothing left to work out. Empty whichever you want calculated.
• The discount comes out negative the final price is higher than the original. That is an increase, and the page reports it as a negative discount rather than pretending otherwise.
• A discount over 100% is refused at 100% the item is free; beyond it the shop would be paying you. If you meant a price rise, swap the two prices.
• The reverse figure is higher than you expected that is the division at work. Taking 20% off and adding 20% back are not the same operation, and the original is always higher than final + percentage.