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Stacked / Double Discount Calculator

Enter an original price and two discounts that stack (the classic case: a store-wide 30% off and an extra 10% off for members, or 30% off plus a 20% coupon on top). The tool applies final = price × (1 − d₁)(1 − d₂) to report the final price, the savings and the equivalent single discount, alongside the naïve d₁ + d₂ figure so you can see exactly how much smaller the real saving is — a difference retailers happily exploit in their advertising.

Final price

315

You save

185

Equivalent single discount

37%

Derived from 1 − (1 − d₁)(1 − d₂); always less than the naïve sum d₁ + d₂.

Price after first discount

350

Naïve sum (common mistake)

40%

Adding the two percentages directly only gives an upper bound — real savings are always smaller.

Formula

Final price = price × (1 − d₁) × (1 − d₂) Equivalent single discount = 1 − (1 − d₁)(1 − d₂) Savings = price − final price Naïve sum (wrong) = d₁ + d₂

Frequently asked

Does "30% off plus an extra 20% off" mean 50% off?

No. The 20% applies to the already-discounted price, not the original. The real math: original × 0.7 × 0.8 = original × 0.56, i.e. 44% off, not 50%. The gap is exactly 30% × 20% = 6%. Retailers like this framing because people instinctively add percentages and assume the saving is bigger than it really is — when you see "an extra X% off", multiply the factors instead of adding the percentages.

Can I use the "equivalent single discount" to directly compare offers from different stores?

Yes — the equivalent single discount is the real percentage you save, so it collapses any stack of discounts into one comparable number. If store A advertises "30% off plus an extra 10% off" (really 37% off) and store B simply offers 35% off, store A is the better deal. The same identity extends to three or more stacked discounts: 1 − (1 − d₁)(1 − d₂)(1 − d₃) …. Caveat: different stores may have different list prices or product specs; the fairest comparison is the actual money you hand over at checkout, not the percentage off.

When does sales tax / VAT come in — before or after the discounts?

In almost every jurisdiction (US state sales tax, Canadian GST/HST, UK VAT, EU VAT, Japan consumption tax, Singapore GST, etc.) tax is added AFTER discounts because the taxable amount is the actual transaction price. The order is: price × (1 − d₁)(1 − d₂) for the discounted subtotal, then × (1 + tax rate) for tax. Two minor exceptions: (1) some US states treat manufacturer coupons specially — the receipt will spell this out; (2) all-inclusive prices already include tax (common in Hong Kong, often in Japan), in which case the discount applies on the tax-inclusive figure and no extra tax step is needed. Use this calculator for the discount step; tax is a single extra multiplication.

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