Double Discount Calculator

Understanding Double and Stacked Discounts

A double discount occurs when two separate discounts are applied sequentially to an item's original price. Retailers frequently offer a storewide sale (such as 20% off) combined with an extra promo code, clearance coupon, or loyalty discount (such as an additional 15% off).

How Double Discounts are Calculated

When two percentage discounts ($d_1\%$ and $d_2\%$) are stacked, the second discount applies to the already reduced intermediate price, not the original price:

$$\text{Intermediate Price } (P_1) = P_0 \times \left(1 - \frac{d_1}{100}\right)$$

$$\text{Final Sale Price } (P_2) = P_1 \times \left(1 - \frac{d_2}{100}\right) = P_0 \times \left(1 - \frac{d_1}{100}\right) \times \left(1 - \frac{d_2}{100}\right)$$

The total effective combined discount percentage ($d_{\text{eff}}$) is always slightly less than simply adding the two percentage numbers together:

$$d_{\text{eff}} = 100\% \times \left[ 1 - \left(1 - \frac{d_1}{100}\right)\left(1 - \frac{d_2}{100}\right) \right]$$

For example, a 20% discount followed by a 15% stacked discount equals a 32% total effective discount rate (not 35%).

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