Discount Calculator

Work out a sale price, the amount saved, and what stacked discounts really come to.

Draft — figures checked, awaiting an editorial read. Not indexed.

Formula: Sale price = original × (1 − first% ÷ 100) × (1 − second% ÷ 100). Stacked discounts multiply; they do not add.

What this calculates

This works out what you actually pay after a discount, and — more usefully — what two stacked discounts really come to. The stacking case is where retail arithmetic and intuition part company. "30% off, plus an extra 20% off sale prices" is not 50% off. The second discount applies to the already-reduced price, so the real saving is 44%. That six point gap is not a rounding difference; on a $120 item it is more than seven dollars.

How it works

The first discount multiplies the original price by one minus the discount as a decimal. The second discount then multiplies *that* result by one minus its own rate. Because the operations multiply rather than add, the combined effect is always less than the sum of the two percentages. The effective discount reported at the bottom is the total saved divided by the original price, which is the number worth comparing against a single-discount offer elsewhere.

Worked example

A $120 jacket at 30% off: 120 × 0.70 = $84. Now apply an extra 20% coupon: 84 × 0.80 = $67.20. Total saved is $52.80, which is 44% of the original, not 50%. Notice also that the order does not matter — applying 20% first and then 30% gives the same $67.20, since multiplication commutes.

Common mistakes

Adding stacked percentages together, as above. Second, calculating a discount from the "was" price when that price was inflated for the sale — the percentage is only meaningful relative to a price something actually sold at, and reference-price rules exist in several jurisdictions precisely because it is so often not. Third, forgetting sales tax, which is applied to the discounted price and so shrinks along with it; a genuine 44% off is 44% off the tax too. Fourth, reading "up to 70% off" as a description of the sale rather than of its single best item — the average reduction across a rack advertised that way is routinely a fraction of the headline, and the only way to know is to check the item in front of you.

Common questions

Is 30% off plus 20% off the same as 50% off?

No. The second discount applies to the already-reduced price, so the combined effect is 44% off, not 50%. On a $120 item that is $67.20 rather than $60.

Does the order of two discounts matter?

No — the arithmetic is multiplication either way, so applying 20% then 30% gives exactly the same price as 30% then 20%. Store policy about which coupons can be combined is a separate matter.