How discounts and sale prices work
Shop signs are easier to read once you know the arithmetic behind them. This guide shows how to find a sale price, check a “was/now” label and handle more than one discount.
Open the Discount CalculatorFinding the sale price
A discount of d% means you pay (100 − d)% of the original price. Multiply the price by that share as a decimal.
sale price = original × (1 − discount ÷ 100)Example: a jacket costs 80 and is 25% off. 80 × 0.75 = 60. You save 20.
Finding the discount from two prices
If a label says “was 120, now 90”, find the saving and divide it by the original.
discount % = (original − sale price) ÷ original × 100(120 − 90) ÷ 120 = 0.25, so it is 25% off. This is useful when offers are expressed differently, such as “save 30” on one item and “20% off” on another.
Why stacked discounts do not add up
If a store takes 20% off and then offers a further 10% off the reduced price, you do not get 30% off. The second discount applies to a smaller amount.
- After 20% off you pay 80% of the price: ×0.80.
- After a further 10% off you pay 90% of that: ×0.90.
- Combined, you pay 0.80 × 0.90 = 0.72, or 72% of the original. The total discount is 28%.
On an item priced at 100, you pay 72, not 70. The order of the two discounts does not change the final price, because multiplication gives the same result either way.
Checking the real saving
A few habits help you judge an offer:
- Convert “save X” offers into a percentage so you can compare them.
- Compare the sale price with what the same item costs elsewhere, not only with the “was” price on the tag.
- Check whether the discount applies before or after tax, delivery or fees, and whether a coupon excludes some items.
A calculator tells you the arithmetic. It cannot tell you whether the “original” price was a price anyone actually paid.
Working backwards to the original price
If you know the sale price and the percentage off, divide by the share you paid. An item costs 54 after 40% off. You paid 60% of the original, so 54 ÷ 0.60 = 90. Adding 40% of 54 would give a wrong answer, because the 40% was taken from the original, not from the sale price.