How to calculate a discount, a sale price and a stacked offer

“30% off, plus an extra 15% for members.” “Was 80, now 60.” “Three for two.” Shops present discounts in many ways, and a minute of arithmetic tells you what each one is really worth.

A single discount

sale price = original × (1 − discount)

20% off 49.99 is 49.99 × 0.8 = 39.99. The saving is the difference, 10.00. The Discount Calculator shows the sale price, the saving and the effective discount together.

Stacked discounts do not add up

When two discounts apply one after another, the second is taken off the already reduced price. A 120 coat with 30% off and then an extra 15%:

1. 120 × 0.70 = 84.
2. 84 × 0.85 = 71.40.

You pay 71.40 and save 48.60 — an effective discount of 40.5%, not the 45% the two numbers seem to promise. Likewise, 20% off and then 10% off is 28% off, not 30%. To combine discounts, multiply what each leaves you to pay: 0.8 × 0.9 = 0.72, so you pay 72%.

Working back to the original price

To check a “was” price, divide the sale price by what is left after the discount. An item at 45 after 25% off was 45 ÷ 0.75 = 60. Adding 25% back on to 45 gives 56.25, which is wrong — the 25% was taken from 60, not from 45.

Is the deal really a deal?

• Compare unit prices. 500 g for 3.50 is 0.70 per 100 g; 750 g for 4.80 is 0.64 per 100 g. The bigger pack without a discount label can be the better buy.
• “Buy one, get one free” is half price per item only if you wanted two. If you needed one, you paid full price for it.
• “Up to 70% off” means some items, usually a few, carry the largest discount.
• Percentages and fixed amounts: 10 off a 40 item is 25% off; 10 off a 200 item is 5%. Convert both to the same terms before comparing offers.

Discounts in your head

• 10% off: move the decimal point one place and subtract. 10% of 64 is 6.40, so the price is 57.60.
• 20% off: double the 10% figure. 20% of 64 is 12.80.
• 25% off: take a quarter. 25% of 64 is 16.
• 15% off: 10% plus half of that again. 6.40 + 3.20 = 9.60.

Close enough for a shop floor; use the calculator when the figure matters.

Discounts and tax

Whether the discount comes before or after tax does not change the total, because both are multiplications. Shops usually discount first and then add tax to the reduced price. To add or remove tax itself, use the Tax Calculator — and remember that taking tax out of a price means dividing, not subtracting.

Discounts as percentage change

A discount is just a percentage decrease, so the Percentage Calculator can confirm one: from 80 to 60 is a 25% decrease. For more on how percentages trip people up, see how to calculate percentage change.