The Stacked Discount Illusion — Why 20% + 10% Off Is Not 30%
When discounts are stacked, the actual discount is smaller than their sum. How to calculate it by multiplying, the order of application, and why order matters when a fixed coupon is mixed with a percentage discount.
'20% off everything, plus an extra 10% for members!' An ad like this feels like 30% off. But the actual discount is 28%, because the second discount applies not to the original price but to the already discounted price.
How it works
Apply a 20% discount and then an extra 10% to an original price of $100,000.
- Step 1: 100,000 × (1 − 0.20) = $80,000
- Step 2: 80,000 × (1 − 0.10) = $72,000
You save $28,000, so the actual discount is 28%. Combining the two discounts into one gives:
Effective discount = 1 − (1 − a) × (1 − b)
For 20% and 10%, that is 1 − 0.8 × 0.9 = 1 − 0.72 = 0.28. The gap from the simple sum (30%) equals the product of the two rates (0.2 × 0.1 = 2%).
The more discounts, the bigger the gap
- 10% + 10% → 19% (simple sum 20%)
- 30% + 20% → 44% (simple sum 50%)
- 50% + 50% → 75% (simple sum 100%, but it is not free)
- 20% + 10% + 5% → 31.6% (simple sum 35%)
'50% off plus an extra 50%' is not free; you pay a quarter of the original price.
Order does not matter between percentage discounts
Whether you apply 20% or 10% first, only the order of multiplication changes, so the result is the same (0.8 × 0.9 = 0.9 × 0.8). However, a store that rounds down the discounted amount at each step to a whole unit may end up a few units off. You can check this difference with the Amount rounding option in the Discount tab.
Order matters when a fixed coupon is mixed in
For an original price of $50,000 with a 20% discount and a $5,000 coupon:
- Coupon first: (50,000 − 5,000) × 0.8 = $36,000
- Discount first: 50,000 × 0.8 − 5,000 = $35,000
Applying the percentage discount first and subtracting the fixed coupon last is better for the shopper, because the $5,000 coupon is not shrunk by the discount rate. The order is set by the seller's policy, so check the terms before paying.
In reverse: hitting a target overall discount
As a seller, if a product is already 20% off and you want the overall discount to be 30%, what extra discount do you need?
Extra discount = 1 − (1 − target) ÷ (1 − existing)
1 − 0.7 ÷ 0.8 = 0.125, so an extra 12.5% discount is needed.
Card cashback and reward points are different
Getting 5% of your payment back as points may look similar to a price discount, but points can only be used on a later purchase and may expire. When comparing, do not add points to a discount as if they were the same; judge separately whether you will actually use them.
Try it in the calculator
In the Discount tab, enter the original price and use Add discount to enter several rates. You will see the amount at each step, the final sale price, the effective discount and how it differs from the simple sum.