What the sale price really is
What the sale price really is
Saving = Price × (Discount ÷ 100)
Sale price = Price − Saving
A $180 item at 30% off saves $54, giving a sale price of $126. The quicker mental route is to work out what you pay rather than what you save: 30% off means paying 70%, and 180 × 0.7 = 126 in one step.
This is the part retailers rely on. “30% off, then an extra 20% off” is not 50% off.
The second discount applies to the already-reduced price. On $180: 30% off gives $126, then 20% off that gives $100.80. A true 50% discount would have given $90. The stacked deal is actually 44% off, not 50%.
The general rule for combining two discounts:
Combined = 1 − (1 − d₁)(1 − d₂)
For 30% and 20%: 1 − (0.7 × 0.8) = 1 − 0.56 = 0.44, or 44% off. The gap widens as the discounts get larger.
A useful reassurance: applying 30% then 20% gives exactly the same result as 20% then 30%, because multiplication is commutative. You do not need to worry about which coupon is scanned first.
What does matter is whether tax is applied before or after the discount. Legitimately, tax should be calculated on the discounted price — you pay tax on what you actually spend. If a receipt shows tax computed on the pre-discount price, that is worth querying.
“Up to 70% off” means at least one item is 70% off. Most will be considerably less.
Buy one get one 50% off is 25% off across two items, not 50% — and only if you wanted both.
Buy two get one free is 33% off across three items.
“Was $180, now $126” depends entirely on whether anything ever sold at $180. Inflated reference prices are common enough that several jurisdictions regulate how long an item must have been offered at the higher price.
The reliable check is not the percentage but the final price compared against what the item costs elsewhere.
If you know the original and sale prices and want the discount percentage:
Discount % = (Original − Sale) ÷ Original × 100
From $180 to $126: (180 − 126) ÷ 180 = 0.30, so 30% off. Note the denominator is the original price — using the sale price would give 42.9%, which is the amount the price would need to rise to get back to $180. Those are different questions with different answers, and mixing them up is the single most common percentage error.
A discount percentage is a statement about the seller's own reference price, which makes it a poor guide on its own. Three checks turn it into useful information.
Compare the final price, not the percentage. An item at 60% off from an inflated starting point can easily cost more than the same item at 20% off elsewhere. The only figure that leaves your account is the final price.
Check the price history. Many products cycle through predictable discount periods. If an item is 30% off every second month, the discounted price is closer to the real price and the “original” is largely notional.
Separate the saving from the spending. A 40% discount on something you did not intend to buy is not a saving of 40% — it is a spend of 60%. The framing matters, because discount marketing is designed specifically to make the first framing feel true.
None of this means sales are not worth using. It means the percentage is the least informative number on the tag, and the final price compared against alternatives is the most.
No. The second discount applies to the already-reduced price, so the combined discount is 44%, not 50%. Multiply the remaining fractions - 0.7 times 0.8 is 0.56, meaning you pay 56% of the original.
No. Applying 30% then 20% gives the identical result to 20% then 30%, because the calculation is multiplication and order does not affect the product.
After. You pay tax on the amount you actually spend, so the discount should be applied first and tax calculated on the reduced price.
25% off across the two items, and only if you genuinely wanted both. Buy two get one free works out to 33% off across three items.