Discount and sale price calculator

The formula

$$S = x\,(1 - d_1)(1 - d_2)$$

$S$ is the sale price, $x$ the original price, and $d_1$, $d_2$ the discounts as decimals (25% is 0.25).

Where it comes from

Taking 25% off leaves 75% of the price, so a single discount multiplies the price by $1 - d_1$. A second discount like “an extra 10% off” applies to the already reduced price, not the original. So it multiplies again by $1 - d_2$.

That means stacked discounts don’t add. The total discount is

$$1 - (1 - d_1)(1 - d_2) = d_1 + d_2 - d_1 d_2$$

which is always a bit less than $d_1 + d_2$. The $d_1 d_2$ term is the second discount’s share of money already taken off.

Worked example

An $80 item, 25% off, then an extra 10%:

$$S = 80 \times 0.75 \times 0.90 = 54.00$$

You save $26, a total discount of 32.5%, not the 35% the signs suggest.

Watch out for

• Order doesn’t matter. 25% then 10% gives the same price as 10% then 25%, because multiplication doesn’t care about order.
• Dollar-off coupons do. “$10 off, then 20% off” gives a different price from “20% off, then $10 off”. Check which one the store applies first.

Last checked November 11, 2026