Why 20% + 10% Off Isn’t 30% Off: Stacked Discount Math
Two discounts don’t add together the way most people assume, and retailers rarely correct the misunderstanding. Here’s the actual math behind stacked discounts, and why the real savings are always smaller than the sum of the percentages.
Why discounts multiply, not add
Each discount applies to whatever price remains after the previous discount, not to the original price. So a second 10% discount is 10% of an already-reduced number, not 10% of the original. This is exactly the kind of math retailers rely on with the pricing psychology tricks covered in our other guide.
The formula
Final Price = Original Price × (1 − Discount1) × (1 − Discount2)Worked example
A $100 item with 20% off, then an additional 10% off:
| Step | Calculation | Price |
|---|---|---|
| Start | — | $100.00 |
| After 20% off | 100 × 0.80 | $80.00 |
| After additional 10% off | 80 × 0.90 | $72.00 |
The final price is $72, a 28% total discount, not the 30% most people assume when they see “20% off” plus “an extra 10% off.” Run your own numbers instantly with our discount calculator, which handles stacked discounts automatically.
Why the gap gets bigger with larger discounts
The difference between “add the percentages” and the real math grows as the discounts get bigger. Two 50% discounts stacked together feel like they should be free, but the real result is 75% off (100 × 0.5 × 0.5 = 25% of original price remains), not 100% off.
Does the order of discounts matter?
No. Multiplication is commutative, so applying 20% off then 10% off gives the exact same final price as applying 10% off then 20% off. The order genuinely doesn’t change the result.
Common mistakes
- Adding percentages together (20% + 10% = 30% off) instead of multiplying the remaining fractions.
- Applying the second discount to the original price instead of the already-discounted price.
- Assuming two 50%-off deals mean free, when the real combined discount is 75%, not 100%.
- Forgetting sales tax is usually calculated after all discounts, not before, which changes the final total further.
Is 20% off plus 10% off the same as 30% off?
No. Stacked percentage discounts multiply the remaining price rather than adding together, so 20% off followed by 10% off equals a 28% total discount, not 30%.
Does the order I apply two discounts in change the final price?
No, multiplying by (1 − 0.20) and then (1 − 0.10) gives the same result as the reverse order, since multiplication order doesn’t affect the product.
How do retailers actually calculate stacked coupon discounts?
Most apply one discount at a time to the running total after the previous discount, exactly matching the multiplicative formula, though policies on which discounts can be combined vary by retailer.
Written by EquateWorld Team
Part of the EquateWorld editorial team.
