Stacked Discount Calculator
Apply up to three sequential discounts and see the true final price, total saved, and real combined discount rate — not the misleading sum.
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The math behind stacked discounts
A store advertises a 20% member discount plus an extra 10% weekend sale. You expect to pay 30% less. You don't. You pay 28% less — and the calculator above shows you exactly why.
Why stacked discounts are not additive
Each discount is applied to the price remaining after all previous discounts have been taken off, not to the original price. That means:
Final Price=P0×(1−d1)×(1−d2)×(1−d3)With a $100 item and discounts of 20% then 10%:
100×0.80×0.90=$72The effective discount is 28%, not 30%. The second 10% discount is 10% of $80 — only $8, not $10.
The effective discount rate
The effective discount rate is the single percentage that produces the same final price as all stacked discounts combined:
e=1−(1−d1)×(1−d2)×(1−d3)For three discounts of 10%, 10%, and 10%:
e=1−0.90×0.90×0.90=1−0.729=27.1%Not 30%. The arithmetic sum always overshoots the real number.
Does the order of discounts matter?
No. Because multiplication is commutative, the order you enter discounts has no effect on the final price or effective rate. Applying 20% then 10% gives exactly the same result as 10% then 20%:
0.80×0.90=0.90×0.80=0.72This matters when a store applies coupons in a fixed order — regardless of that order, the math is the same.
Real-world examples
Black Friday + loyalty card: A $200 jacket is 30% off for Black Friday, then a further 15% off with your store card. Final price: $200 × 0.70 × 0.85 = $119. Effective discount: 40.5% — not 45%.
Clearance + coupon code: A $50 item is already 40% off on the clearance rack. You have a 20% off coupon. Final price: $50 × 0.60 × 0.80 = $24. Effective discount: 52% — not 60%.
Employee discount + sale: An item priced at ¥10,000 carries a 25% employee discount plus a 10% seasonal sale. Final price: ¥10,000 × 0.75 × 0.90 = ¥6,750. Effective discount: 32.5% — not 35%.
When does a combined discount break even?
If a retailer offers a single combined discount instead of stacking them, you can find the equivalent by plugging into the effective-rate formula. A 20% + 10% stack equals a flat 28% discount — so a sign that reads "save 30%" is giving you a slightly better deal than two separate percentage signs that add up to 30%.
The third discount (optional)
Leaving the third discount at 0% has no effect on the calculation — multiplying by (1 − 0) = 1 changes nothing. Use it when you have a third coupon, a cashback reward percentage, or a bundled rebate to layer on top of the first two.
Frequently Asked Questions (FAQ)
How does the stacked discount formula work?
Each discount is applied to the price remaining after all previous discounts. The formula is:
Final Price = Original × (1 − d₁) × (1 − d₂) × (1 − d₃)
Example with 20% and 10%: $100 × 0.80 × 0.90 = $72. The discounts multiply, they do not add.
Does 20% + 10% equal a 30% discount?
No. When discounts are applied in sequence, a 20% discount followed by a 10% discount gives an effective rate of 28%, not 30%. The second discount is taken off the already-reduced price, not off the original. The correct calculation is: 1 − (1 − 0.20) × (1 − 0.10) = 1 − 0.72 = 0.28, or 28%.
What is the effective discount rate?
The effective discount rate is the single percentage that produces the same final price as all the stacked discounts combined. For example, 20% + 10% stacked gives an effective rate of 28%. It is always lower than the arithmetic sum of the individual discounts because each subsequent discount is applied to a smaller base amount.
Does the order of the discounts matter?
No. Because multiplication is commutative, applying 20% then 10% gives exactly the same result as applying 10% then 20% — both yield a 28% effective discount and the same final price. The order shown here is purely for clarity.
Disclaimer
Results assume discounts are applied sequentially to the running price, not to the original price independently (multiplicative stacking). If a retailer applies each discount to the original price separately, use the effective-discount formula for each and combine.