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    Calculates locally in your browser · stacked discounts and tax
    Retail / markdown arithmetic

    Discount and final price

    Apply one or two discounts in sequence, then tax, and see the true effective markdown. The point of the page is the gap between the advertised percentages and the discount you actually receive.

    Stacking20% → 10%Rate gap2.00 ptsPay ratio72.0%
    Final price
    $86.40
    Before sales tax
    Total saved
    $33.60
    Off a $120.00 list price
    Effective discount
    28.00%
    Not 30.0% — discounts multiply
    Payable with tax
    $93.53
    $7.13 of sales tax
    Discount stack, step by step
    Each discount applied to the already-reduced price, then tax on what is left.
    28.0% off
    Discount stack, step by step
    StepAmountChange
    List price$120.00—
    After 20% off$96.00−$24.00
    After extra 10% off$86.40−$9.60
    Total saved$33.6028.00% of list
    Sales tax$7.138.250% of the reduced price
    Payable$93.53Discounted price + tax

    Adding the two rates would suggest 30.0% off. Stacking gives 28.00% — the second discount applies to a smaller base.

    Inspect the model
    Choose a quick result view, a scaled comparison, or the complete diagnostic set.
    Price waterfall
    List price reduced twice, then tax added back.
    Price waterfall$0$28$57$85$113$142$120ListList$96After 1stAfter 1st$86After 2ndAfter 2nd$94With taxWith taxAmount
    Final price vs discount depth
    A single discount of the same size, for comparison.
    Final price vs discount depth$0$26$51$77$102$1285%5%10%10%15%15%20%20%25%25%30%30%40%40%StackedSingle
    Canonical equations
    The exact relationships implemented by this engine.

    P₁ = P(1 − d₁) · applied to list price

    P₂ = P₁(1 − d₂) · applied to the reduced price

    1 − (1−d₁)(1−d₂) · always below d₁ + d₂

    P₂(1 + t) · tax is charged on the discounted price

    finance methodology

    A clear path from inputs to results.

    Retailers advertise discounts that stack, and stacked percentages do not add. Twenty percent followed by ten is 28% off, not 30%. This engine applies each discount to the already-reduced price and reports the true markdown.

    Step-by-step methodWorked exampleAssumptions explained

    How to use

    1. Enter the list price.
    2. Set the first discount — the headline percentage.
    3. Set the second discount if the offer is “extra X% off reduced prices”.
    4. Add the sales tax rate so the payable amount is correct.
    5. Compare the effective discount with the sum of the two rates.

    The formula

    P1=P(1−d1),P2=P1(1−d2),effective=1−(1−d1)(1−d2)P_1 = P(1-d_1), \quad P_2 = P_1(1-d_2), \quad \text{effective} = 1-(1-d_1)(1-d_2)

    Reference: Standard retail markdown arithmetic (Horngren et al., Cost Accounting).

    Worked example

    $120 with 20% then a further 10%, plus 8.25% tax

    Inputs
    • List price $120.
    • First discount 20%, second discount 10%.
    • Sales tax 8.25%.
    Calculation path
    1. 1

      After the first discount: 120 × 0.80 = $96.

    2. 2

      After the second: 96 × 0.90 = $86.40.

    3. 3

      Total saved: $33.60, which is 28.0% of list — not 30%.

    4. 4

      Tax on the reduced price: 86.40 × 0.0825 = $7.13.

    5. 5

      Payable: $93.53.

    Result

    $86.40 before tax · 28.0% effective discount · $93.53 payable.

    Interpreting the result

    The shortfall from 30% to 28% comes from the second discount applying to a base that has already shrunk. The gap grows with the size of the discounts: 50% then 50% is 75% off, not 100%. Any offer above two stacked percentages should be checked this way before you believe the headline.

    Assumptions & limitations

    • Both discounts are percentages, so their order does not matter. Fixed-dollar coupons do not commute with percentages.
    • Tax applies to the discounted price, which is the rule in most jurisdictions.
    • No minimum spend, membership tier or excluded-brand conditions are modelled.
    • The list price is the genuine pre-discount price, not an inflated reference.

    Frequently asked questions

    Why is 20% + 10% only 28%?

    Because the second 10% applies to the already-discounted price. Algebraically 1 − (1−0.2)(1−0.1) = 0.28. The rates multiply as survival factors, not add.

    Is tax charged before or after the discount?

    After, in most jurisdictions. Tax is due on the price actually paid, so the discount reduces the taxable amount.

    Does the order of discounts matter?

    Not for percentage discounts — multiplication is commutative. It matters for fixed-dollar coupons: a $20 coupon before 20% off is worth more than the same coupon after.

    How do I compare a percentage-off offer with a fixed-dollar one?

    Convert both to the same basis: compute the final price under each and compare. A $30 coupon beats 20% off a $120 item ($24) but loses to 20% off a $200 item ($40).

    Methodology last reviewed 2026-10-18. Results are informational and not financial or engineering advice — see our disclaimer.