How to Calculate a Discount and the Sale Price

A discount is a percentage taken off a price. The maths is a percentage decrease, but the questions people ask are practical: what will I pay, how much do I save, and how good is this deal?

Sale price from a percentage discount

Discount amount = price × (discount ÷ 100)
Sale price      = price − discount amount
             or = price × (1 − discount ÷ 100)

A coat costs 120 and is 25% off. The discount is 120 × 0.25 = 30, so the sale price is 90. Or in one step, 120 × 0.75 = 90.

Finding the discount percentage from two prices

Discount % = (original price − sale price) ÷ original price × 100

Something was 60 and is now 42. The saving is 18, and 18 ÷ 60 = 0.3, so it is 30% off.

Stacked discounts

Shops often advertise "30% off, plus an extra 10% at the till". The second discount applies to the price after the first, so the two do not add to 40%.

The total saving is 29.60, which is 37% of 80, not 40%. The order does not change the final price, because multiplication is commutative, but the discounts never simply add.

Adding sales tax

Check whether a price includes tax. In many places advertised prices exclude sales tax, which is added at the till. To add 8.25% tax to 49.99, multiply by 1.0825: 49.99 × 1.0825 = 54.11.

Common mistakes

• Adding stacked discounts together.
• Working out the discount on the sale price instead of the original price.
• Comparing deals by the percentage alone. A 50% saving on something you did not need is still money spent.

The discount calculator handles up to three stacked discounts and shows the effective percentage off.

Try it yourself

1. What is the sale price of a 65 item at 40% off?
2. An item was 90 and is now 63. What is the discount?
3. A 200 item is 25% off, then an extra 20% off the reduced price. What is the final price and the effective discount?

Answers: (1) 39; (2) 30%; (3) 120, which is an effective 40% off.