How Percentage Discounts Work

A store advertises "30% off," and right next to it, another sign says "20% off, plus an extra 10% off at checkout." Those sound like the same deal. They aren't — the second one is a smaller discount, even though 20 + 10 = 30. Understanding why comes down to how percentage discounts are actually calculated.

What a percentage discount means

A percentage discount removes a percentage of the original price, not a fixed dollar amount. A 20% discount on a $50 item removes $10; the same 20% discount on a $200 item removes $40. The percentage stays constant; the dollar amount it represents scales with the price.

The discount formula

Discount Amount = Original Price × (Discount Percentage ÷ 100)

Final Price = Original Price − Discount Amount

The sale price formula (direct method)

Instead of calculating the discount and subtracting it in two steps, you can go straight to the final price by multiplying by the remaining percentage:

Final Price = Original Price × (1 − Discount Percentage ÷ 100)

A 20% discount leaves 80% of the price, so you can multiply directly by 0.80. This is the same method our discount calculator and sale price calculator use internally.

Worked examples

A $60 jacket at 10% off:

Discount = 60 × 0.10 = $6. Final price = 60 − 6 = $54.

A $60 jacket at 20% off:

Discount = 60 × 0.20 = $12. Final price = 60 − 12 = $48.

A $60 jacket at 50% off:

Discount = 60 × 0.50 = $30. Final price = 60 − 30 = $30.

Stacking multiple discounts

Retailers sometimes apply two discounts in sequence — for example, a storewide 20% off, then an additional 10% off at checkout. Each discount is applied to the result of the previous one, not to the original price:

A $100 item, 20% off: $100 × 0.80 = $80.

Then an additional 10% off that $80: $80 × 0.90 = $72.

The combined discount removed $28 from $100 — an effective discount of 28%, not 30%.

Why discounts aren't simply added

The second discount is calculated on an already-reduced price, so it removes a smaller dollar amount than it would have on the full original price. You can see the pattern by multiplying the "remaining" factors together instead of adding the percentages:

0.80 × 0.90 = 0.72 → a 28% total discount, not 20% + 10% = 30%.

This is the same underlying mechanism explained in why a 20% increase and decrease don't cancel out — percentages compound off whatever the current value is, not the original one.

Comparing two offers

Given the example above, a flat 30% off $100 would leave a final price of $70 (100 × 0.70). The "20% + 10%" stacked offer leaves $72. The flat 30% discount is actually the better deal, even though the two numbers (20+10 vs. 30) look equal on a sign. The only reliable way to compare stacked and flat discounts is to calculate the actual final price for each, not to add the percentages.

Discount percentage vs. actual savings

A "50% off" sign always means the same relative reduction, but the dollar value of that reduction depends entirely on the original price — 50% off a $20 item saves $10; 50% off a $2,000 item saves $1,000. A higher percentage doesn't automatically mean a bigger discount on your specific purchase if the base price is lower; it's worth checking both the percentage and the actual final price, especially when comparing similar items at different starting prices. If you know the sale price and want to work out what the original price was, see our guide on finding the original price after a discount.