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Discount Math: Percentage Off, Stacked Discounts, and Markup vs. Margin

Calculating a single discount is easy. Stacked discounts and the markup-vs-margin mix-up are where the math quietly stops behaving the way most people expect.

  1. Sale price = original price x (1 - discount rate)

    To find a sale price directly, convert the percentage to a decimal, subtract it from 1, and multiply by the original price. A $80 item at 25% off is $80 x 0.75 = $60.

  2. Working backward: find the discount rate from two prices

    If you know the original and sale prices but not the percentage, the formula flips: discount rate = (original - sale) / original. A $50 item now selling for $35 is a (50-35)/50 = 30% discount.

  3. Stacked discounts multiply, they don't add

    Two "20% off" and "10% off" promotions applied in sequence do not equal 30% off. The math compounds: $100 x 0.80 x 0.90 = $72, a 28% total discount, not 30%, because the second discount applies to an already-reduced price.

  4. "50% off, then 50% off again" isn't free

    A common intuition trap: two separate 50%-off discounts applied in sequence result in 75% off total, not 100% off, since the second half is taken from the already-halved price.

  5. Markup and margin describe the same gap differently

    A 50% markup (price = cost x 1.50) is not the same as a 50% margin (profit is 50% of the selling price). An item costing $100 with a 50% markup sells for $150, but that $50 profit is only a 33% margin relative to the $150 sale price.

Why stacked promotions rarely add up the way ads imply

Retailers sometimes advertise combinable discounts in a way that lets shoppers assume the percentages simply add, but because each discount applies to the already-discounted price left by the one before it, the true combined discount is always somewhat lower than the sum of the individual percentages.

Where the markup vs. margin confusion actually costs people money

Because markup is calculated against cost and margin is calculated against selling price, the two numbers diverge more as the percentage gets larger, and mixing them up when pricing a product or evaluating a deal can lead to meaningfully overestimating actual profit or savings.

Frequently Asked Questions

How do I calculate the original price if I only know the sale price and discount percentage?

Divide the sale price by (1 minus the discount rate as a decimal). If an item is $60 after a 25% discount, the original price was 60 / 0.75 = $80.

Is a 20% markup the same as a 20% margin?

No. A 20% markup on a $100 cost item prices it at $120, which works out to a 16.7% margin, not 20%, because margin is measured against the selling price rather than the cost. The two only converge toward each other at very small percentages.