Stacked Discounts: Why 20% + 10% Is Not 30%
How stacking two discounts actually works, the true discount rate behind common combinations, and how to spot when a 'double discount' deal is worse than it looks.
Sale season brings out the “extra 10% off already-reduced prices!” banners. Retailers know most shoppers add the numbers together — and that this mental shortcut works in the store’s favor.
The actual math of stacking
Discounts multiply; they don’t add. A 20% discount followed by another 10% off the already-reduced price:
$100 → −20% → $80 → −10% → $72
The true discount is 28%, not 30%. Why? Because the second discount applies to a smaller base. You save $8 on the second step, not $10, since 10% of $80 is $8.
The general formula
For discounts d₁ and d₂ (as decimals):
Effective discount = 1 − (1 − d₁)(1 − d₂)
For 20% + 10%: 1 − (0.8 × 0.9) = 1 − 0.72 = 0.28 = 28%.
A useful shortcut: the combined discount always equals the sum minus the product of the two rates. 20% + 10% → 0.2 + 0.1 − 0.02 = 0.28.
Common combinations, true rates
| Stacked discount | Feels like | Actually |
|---|---|---|
| 20% + 10% | 30% | 28% |
| 30% + 20% | 50% | 44% |
| 50% + 20% | 70% | 60% |
| 25% + 25% | 50% | 43.75% |
| 50% + 50% | 100% | 75% (!) |
That last row is the eye-opener: two half-price discounts in sequence still leave you paying a quarter of the original price. No retailer is ever giving stock away.
When stacking is still a good deal
None of this means stacked discounts are bad — 44% off is a genuinely strong discount. It means:
- Compare true rates, not banners. “50% + 20%” (60%) is worse than a flat “65% off.”
- Watch which base the second discount applies to. Some stores apply the extra percentage to the original price — in that rare case, the discounts do add. Read the fine print; ambiguity here is usually intentional.
- Coupon stacking apps exploit this constantly. “We stacked five discounts!” — the combined rate is never what the sum suggests.
A final gotcha: percentage increases don’t reverse
The same asymmetry applies to price rises. A price that rises 25% and then falls 25% doesn’t return to the start:
$100 → +25% → $125 → −25% → $93.75
Down 6.25% overall. Percentages describe a change relative to whatever the base is at that moment — which is why they never simply cancel.
Check a deal before you celebrate it
Enter the original price and both discounts into the Discount Calculator — it computes the true stacked rate, the final price and your actual savings, so you know exactly how good (or mediocre) that “double discount” really is.