Discount calculator

Why stacked discounts are smaller than they look

“20% off, plus an extra 20% off sale prices” sounds like 40%. It is 36%. The second discount is taken from the price after the first one, not from the original: 100 falls to 80, and 20% of 80 is 16, leaving 64.

The gap widens as the discounts get larger. Two 50% discounts are 75% off, not 100%, half of a half is a quarter, and a quarter of the price is still left to pay. This is the single most common mistake in reading a sale, and it is the reason the extra discount is a separate field here rather than something to add on yourself.

Order, and when it matters

Two percentages can be applied in either order and give the same answer, because multiplying by 0.7 and then 0.9 is the same as multiplying by 0.9 and then 0.7. A fixed amount mixed with a percentage is different: taking 20 off and then halving is not the same as halving and then taking 20 off. Shops almost always apply the percentage first, which is the less generous of the two.

Tax, and when to leave it blank

Whether to fill in the tax field depends entirely on where you are. In the United States sales tax is added at the till, so the shelf price is pre-tax and entering the rate here gives the figure on the receipt. In the UK, across the EU and in most of the world, VAT is already inside the advertised price, entering it would charge it twice.

Where tax does apply, it is charged on the discounted price rather than the original, because you are taxed on what you actually pay. A discount therefore reduces the tax as well. Tax is shown as its own line and is never counted as part of the saving.

Checking a sale claim

The second mode works backwards from two prices: what was it listed at, and what did it actually come to. That is the useful direction when a sign says “up to 70% off” and you want to know what you were really given, or when a price has been raised before a sale so that the discount is measured against a figure nobody paid.

To go the other way, a sale price back to the original, divide by 1 minus the discount as a decimal. A price of 56 after 30% off was 80, not 72.80. Adding the percentage back on gives the wrong answer because it is being taken from the smaller number.