Discount Calculator

Three questions, three calculations

What is the sale price at X percent off? What percentage off is this, given the original and sale price? And what was the original price, given the sale price and the discount? All three are simple, and people routinely reach for the wrong one, particularly the third.

Stacked discounts multiply, they do not add

An extra 20 percent off an already 30 percent reduced item is not 50 percent off. Multiplying by 0.7 and then by 0.8 gives 0.56, so the total reduction is 44 percent. Retailers rely on the intuition that the percentages add, because it makes the second discount feel larger than it is. The same arithmetic applies to a coupon on a sale price.

Reversing a discount requires division

If an item sold for 60 after 25 percent off, the original was 60 divided by 0.75, which is 80. It was not 60 plus 25 percent, which gives 75. Adding the percentage back applies it to the wrong base, and the error grows with the discount size. This is the single most common mistake in discount arithmetic.

Percentage off versus multiples of price

Buy-one-get-one-free is 50 percent off when you want both items and 0 percent off when you only need one. Three for the price of two is 33.3 percent off, not 50. Converting every offer to an effective unit price is the only reliable way to compare, and it frequently reveals that a smaller headline percentage is the better deal.

Tax, and what the discount applies to

In most jurisdictions tax is calculated on the discounted price, so the saving is slightly larger than the sticker reduction suggests. Where tax is included in displayed prices, the discount already accounts for it. Check whether a coupon applies before or after shipping too, since that changes the total materially on smaller orders.

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