Stacked Discounts Explained: Why 20% Off Plus 10% Off Is Not 30% Off

A shop advertises 20 percent off, and at the till an extra 10 percent comes off the reduced price. Is that 30 percent? It is not, and the difference is why some offers are better than they sound and others worse. Discount maths is mostly four small formulas used in the right order.

One discount

A discount of d percent leaves you paying (100 − d) percent of the price.

Sale price = original price × (1 − d ÷ 100). Savings = original price − sale price.

For a $150 jacket at 20 percent off, you pay $150 × 0.80 = $120 and save $30. The Discount Calculator shows the sale price, the saving and the total at once.

Two discounts, one after the other

When a second discount applies to the price that is already reduced, you multiply the remaining shares.

• First discount: 20 percent off $150 leaves $120.
• Second discount: 10 percent off $120 takes off $12 and leaves $108.
• Total saving: $42, which is 28 percent of $150, not 30.

The combined effect of two discounts of a and b percent is 100 − (100 − a)(100 − b) ÷ 100. For 20 and 10 that is 100 − 80 × 90 ÷ 100 = 28.

Even large stacks have a ceiling. Two 50 percent discounts on an $80 item leave $20, which is 75 percent off in total, not 100.

Adding sales tax

Tax is normally charged on the price after discounts. With the 20 and 10 percent stack on $150, the pre-tax price is $108. At 8 percent sales tax, the tax is $8.64 and you pay $116.64. The calculator has an optional tax field for this. If your shop works out tax before the discount, check the receipt, because the order changes the result slightly. For the tax formula alone, see how to add and remove sales tax.

Finding the original price

Suppose the sale price is $120 after 20 percent off. What was the original price?

Original price = sale price ÷ (1 − d ÷ 100) = 120 ÷ 0.80 = $150.

A common wrong answer is 120 × 1.20 = $144. That adds 20 percent to the sale price, but the 20 percent was taken from the larger original price. The calculator has a mode for this reverse calculation.

Finding the discount percentage

If something was $150 and is now $120, the discount is (150 − 120) ÷ 150 × 100 = 20 percent. Divide by the original price, not the sale price. The same method works for price rises, and a rise is shown as a negative discount. For percentage changes in general, see percentage change vs percentage points.

Comparing offers

1. Convert each offer to a final price on the same item.
2. Add shipping and tax to each.
3. Ignore the size of the advertised percentage and compare pounds, dollars or rupees.
4. Check whether a coupon works on sale items, and whether it applies to the full price or the reduced one. Some exclude sale items entirely.
5. If you want to know how a discount affects a seller's margin, the Profit Margin Calculator shows the other side, and the Percentage Calculator checks any percentage you are unsure about.

Quick reference