How Discounts and Sale Prices Work — A Complete Guide

A discount is a reduction from the usual price, usually given as a percentage. When a shop says "30% off", it does not mean you pay 30% of the price. It means 30% is taken away, and you pay the remaining 70%. That one distinction is the source of almost every discount mistake, so it is worth fixing in your mind first: the discount percentage is what you save, and 100 minus that percentage is what you actually pay.

The two numbers every discount gives you

Every discount calculation produces two useful numbers. The first is the amount saved, which is the original price multiplied by the discount percentage and divided by 100. The second is the final price, which is the original price minus the amount saved. You can also reach the final price in one step by paying the remaining percentage directly: for a 30% discount, pay 70% of the original price. Both routes must agree, and checking them against each other is a quick way to catch an error.

Worked example 1: a jacket at 30% off

Suppose a jacket costs 120 and is reduced by 30%. The amount saved is 120 × 30 ÷ 100 = 36. The final price is therefore 120 − 36 = 84. Using the one-step route, you pay 70% of 120, which is 120 × 70 ÷ 100 = 84. The two methods agree, which is exactly what you want to see. If you are in a shop and need a fast estimate, find 10% first: 10% of 120 is 12, so 30% is three times that, 36, and the price after the discount is 84.

Worked example 2: comparing two deals

Imagine one shop offers a television at 500 with 20% off, and another offers the same model at 460 with 10% off. The first deal saves 500 × 20 ÷ 100 = 100, so the final price is 400. The second deal saves 460 × 10 ÷ 100 = 46, so the final price is 414. The first shop is cheaper, even though its starting price was higher. This is why comparing only the discount percentage, or only the starting price, can mislead you. Always compare the final prices.

Worked example 3: working backwards from a sale price

Sometimes you know the sale price and the discount, and you want the original price. If a pair of shoes costs 63 after a 30% discount, you paid 70% of the original price. So the original price is 63 ÷ 70 × 100 = 90. A useful check is to go forwards again: 30% of 90 is 27, and 90 − 27 = 63. Working backwards is a common exam question and a genuinely useful shopping skill, because sale labels do not always show the original price clearly.

Successive discounts are not added together

One of the most common traps is a "further 20% off" applied after an earlier discount. A 30% discount followed by a further 20% discount is not a 50% discount. The second discount applies to the already reduced price, not to the original price. Take an item that costs 100. After 30% off it costs 70. A further 20% off 70 saves 14, giving a final price of 56. The total saving is 44, not 50. Shops are allowed to advertise the two discounts separately, but your wallet only cares about the final price.

Common mistakes to avoid

First, do not confuse the discount with the amount you pay: 30% off means you pay 70%, not 30%. Second, do not add successive discounts together, as shown above. Third, be careful with tax and delivery charges, which are usually added after the discount, so the amount at the checkout can be higher than the discounted price on the label. Fourth, watch for "up to 50% off" signs: the largest discount in the sale may apply to only a few items, while the item you want may be reduced by much less.

A quick method for mental maths

For everyday shopping, the 10% method is usually enough. Find 10% by moving the decimal point one place to the left, then build the discount from tens and fives. For a 25% discount, find 10%, double it for 20%, halve the 10% figure for 5%, and add them. On a price of 80, 10% is 8, 20% is 16, 5% is 4, so 25% is 20, and the final price is 60. With a little practice this becomes faster than reaching for a calculator, and it also gives you a rough check on any figure a till or website shows you.

Frequently asked questions

What is the difference between a discount and a sale price?

The discount is the amount taken off, and the sale price is what remains. On a 120 item at 30% off, the discount is 36 and the sale price is 84.

Is 50% off the same as half price?

Yes. A 50% discount means you save half and pay half, so a 200 item costs 100. This is the one percentage where the discount and the amount you pay are equal.

How do I check a discount quickly?

Work out the amount saved and the final price by two different routes if you can, for example by finding the saving and subtracting it, and also by paying the remaining percentage directly. If the two answers differ, one of them is wrong.

Can a discount ever be more than 100%?

In ordinary shopping, no. A 100% discount means the item is free. Anything described as more than 100% off is either a mistake or a different kind of offer, such as a refund larger than the price, which is not a normal discount.

Try it yourself with the Discount Calculator, and if you want the general method behind all of this, read How to Calculate a Percentage.