Why 20% Off and Then 10% Off Does Not Equal 30% Off
A sign says 20% off, and at the register a coupon takes another 10% off. It is tempting to call that 30% off, but the total saving is smaller. The second discount applies to a price that is already lower, so it removes less money than the same percentage would have at the start.
This article shows the rule for stacking percentage discounts, a table of common combinations, what changes when one of the discounts is a flat dollar amount, and how to work out the second discount you would need to reach a target price.
Discounts multiply, they do not add
A discount of d% leaves you paying (100 − d)% of the price. Two discounts in a row leave you paying the product of the two shares.
total discount = 1 − (1 − d₁) × (1 − d₂)Use decimals: 20% is 0.20. Add more factors for more discounts.
Worked example: a $100 item, 20% off, then 10% off. After the first discount you pay 100 × 0.80 = $80. After the second you pay 80 × 0.90 = $72. The total saving is $28, or 1 − 0.80 × 0.90 = 28%, not 30%.
Because multiplication does not depend on order, two percentage discounts give the same final price either way round. Taking 10% off first and then 20% still gives 100 × 0.90 × 0.80 = $72.
Common combinations
| First discount | Second discount | Price paid on $100 | Total saving |
|---|---|---|---|
| 10% | 10% | $81.00 | 19% |
| 20% | 10% | $72.00 | 28% |
| 25% | 25% | $56.25 | 43.75% |
| 30% | 20% | $56.00 | 44% |
| 50% | 20% | $40.00 | 60% |
| 50% | 50% | $25.00 | 75% |
The shortfall against simple addition grows with the size of the discounts. Two 10% discounts fall 1 point short of 20%, while two 25% discounts fall about 6 points short of 50%.
Three or more work the same way. For 20%, 10% and 5%, multiply 0.80 × 0.90 × 0.95 = 0.684, so you pay 68.4% of the original price and save 31.6%.
When order matters: dollar amounts
Order stops mattering only when every discount is a percentage. A flat amount such as $10 off does not scale with the price, so the sequence changes the result.
- Dollar coupon first, then 20% off: (100 − 10) × 0.80 = $72.
- 20% off first, then the dollar coupon: 100 × 0.80 − 10 = $70.
The percentage-first order costs $2 less, because the percentage takes a bigger bite out of the full price. Stores set the order in their terms, so read how a coupon is applied before assuming which you will get.
Reading the wording and the tax
Phrasing decides which rule applies. "Take an extra 10% off the sale price" multiplies, as above. An offer that says "20% off, plus 10% of the original price" is different: both amounts come from the same starting number, so on $100 you save 20 + 10 = $30 and pay $70. When the wording is unclear, ask the seller or price a test item at the register.
Sales tax normally comes last, on the discounted price. Worked example: a $100 jacket at 25% off costs $75, a 10% member discount takes it to $67.50, and 8% sales tax makes the final total 67.50 × 1.08 = $72.90. The two discounts together saved 32.5%, not 35%.
Working out the discount you still need
Suppose you want to pay no more than 60% of the original price, meaning a 40% total saving, and you already have a 30% discount. The remaining share to pay is 0.60 ÷ 0.70 = 0.857, so you need a second discount of 1 − 0.857 = 14.3%, not 10%.
In dollars the check is easy: $100 at 30% off is $70, and 14.3% off $70 is $10, leaving $60.
To undo the stack, divide the final price by the combined share. A final price of $72 after 20% then 10% off comes from $72 ÷ 0.72 = $100. Our guide to finding the original price before a discount or tax covers that in detail, and the percent decrease calculator finds the total drop between two prices.
Stacking is also why a rise followed by an equal fall does not return you to the start, as explained in percent change versus percentage points. To price one discount at a time, use the discount calculator or the percent off calculator, and feed each result into the next.
These examples are illustrations, not financial advice. Retailers decide which offers can be combined, so check the terms before you rely on a stacked saving.
- Discount Calculator: Choose whether to apply a discount to a price or to find the discount between two prices. Pick the type of offer, enter the prices and see what you pay, what you save and the discount as a percentage.
- Percentage Decrease Calculator: Choose whether you want to take a percentage off a number or find the percentage drop between two values, fill in the fields and press Calculate. The guide below shows the formula and several worked cases.
- Percent Off Calculator: Enter the percent off and the original price to see the final price and your saving. Switch the mode to find the percentage discount when you already know both prices.
This article is general information, not professional advice. See our Disclaimer and Editorial Policy.
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