How percentage discounts actually work (and why "30% off" isn't always what it seems)

Percentage discounts look simple, but the math behind sales, markdowns, and stacked discounts trips up more people than you'd expect. Here's what's actually happening behind that "% OFF" sign.

The basic formula

A percentage discount reduces a price by a fraction of itself. If an item costs $80 and is 25% off, you calculate the discount amount first: 80 × 0.25 = $20. Subtract that from the original price: 80 − 20 = $60. That's your final price.

The shortcut: multiply the original price by (1 − discount rate). For 25% off, that's 80 × 0.75 = $60 — same answer, one step.

Why "stacked" discounts don't add up the way you'd think

This is where most people get tripped up. If a store offers 20% off, then an extra 10% off at checkout, you might expect 30% off total. You'd be wrong.

Discounts stack multiplicatively, not additively. Starting at $100: 20% off brings it to $80. Then 10% off of $80 (not the original $100) brings it to $72. That's a total discount of 28%, not 30% — because the second discount applies to the already-reduced price.

This matters more than it seems: the bigger the first discount, the smaller the real value of the second one in absolute terms, even though the percentage stays the same.

Percentage increase works the same way, in reverse

If a $50 item goes up by 20%, the new price is 50 × 1.20 = $60. But if it then drops by 20% from $60, it does NOT return to $50 — it goes to 60 × 0.80 = $48. Percentage increases and decreases are not symmetric, because each one is calculated on a different base amount.

Reverse-calculating: finding the original price

Sometimes you know the sale price and the discount percentage, and need the original price. If something costs $45 after a 25% discount, the $45 represents 75% of the original price (since 100% − 25% = 75%). So: original price = 45 ÷ 0.75 = $60.

This reverse calculation is useful for spotting fake "sales" where the "original price" was inflated to make the discount look bigger than it is.

Try it yourself

Our percentage calculator handles discounts, increases, and reverse calculations instantly — useful for checking whether a "deal" is actually as good as it's advertised.

This article is for general education and does not constitute financial or shopping advice.