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Stacked Discount Calculator — Why 20% + 10% Isn't 30%
Successive (stacked) discounts do not add up — they multiply. A "20% off, then an extra 10% off" deal is not 30% off; it is 28% off, because the second discount applies to the already-reduced price, not the original. Take $100: 20% off brings it to $80, then 10% off $80 takes off just $8, landing at $72 — a $28 saving, an effective 28% discount. The rule is sale = price × (1 − d₁) × (1 − d₂) × …, and the effective discount is 1 − the product of the surviving fractions. Most simple calculators refuse stacked discounts and punt you to a separate tool; this mode applies them multiplicatively and shows the true effective percentage so you are not fooled by a headline that sounds bigger than it is. Free, no login.
Stacked formula: sale = price × (1 − d₁) × (1 − d₂) × … (multiplicative, never additive)
- Effective discount = 1 − (1 − d₁)(1 − d₂)… — always LESS than the naive sum of the rates
- Worked example — $100, 20% then 10%: 100 × 0.80 × 0.90 = $72 → 28% effective (not 30%)
- Step-by-step — 20% off $100 = $80; then 10% off $80 = $8; final $72, saving $28
- Worked example — $200, 25% then 15%: 200 × 0.75 × 0.85 = $127.50 → 36.25% effective (not 40%)
- Order of two %-discounts does not change the result (0.8 × 0.9 = 0.9 × 0.8)
- A fixed $-amount mixed with %-discounts DOES depend on order — apply and check both ways
Frequently asked questions
Does a 20% then 10% discount equal 30% off?
No — it equals 28% off. Stacked discounts multiply rather than add, because the second discount is taken off the already-reduced price. On a $100 item, 20% off gives $80, and 10% off $80 removes only $8, leaving $72. That is a $28 saving, so the effective discount is 28%, not the 30% you would get by adding the two rates. The general rule is sale = price × (1 − d₁) × (1 − d₂), and the effective discount is 1 − (1 − d₁)(1 − d₂). The naive sum always overstates the real saving.
How do I calculate the effective rate of stacked discounts?
Multiply the surviving fractions and subtract from one. For discounts of 20% and 10%, the surviving fractions are 0.80 and 0.90; their product is 0.72, so 72% of the price remains and the effective discount is 1 − 0.72 = 28%. For three discounts of 30%, 20% and 10%: 0.70 × 0.80 × 0.90 = 0.504, an effective 49.6% discount — not the 60% the rates might suggest. This calculator does the multiplication for you and reports both the final price and the true effective percentage.
Does the order of stacked discounts matter?
For percentage discounts, no — multiplication is commutative, so 20% then 10% gives the same $72 as 10% then 20%. Order only matters when you mix a fixed dollar-amount discount with percentage discounts: taking $10 off before a 20% discount is not the same as taking it off after, because the percentage acts on a different base. When a fixed amount is involved, decide the intended sequence and apply it consistently; for percentage-only stacks you can combine them in any order.