Discount Calculator

A 20% discount followed by an additional 10% off isn't a 30% discount — it's roughly 28%, because the second discount applies to the already-reduced price rather than the original one. Each successive discount multiplies against a progressively smaller base, so stacked percentage-off deals are always worth a little less than their sum suggests. This is one of the most common places people misjudge a "deal," especially during layered sales events like a storewide discount combined with a coupon or loyalty discount.

The gap between the "naive sum" and the true combined discount grows as either discount gets larger. Two 10% discounts stacked together produce a combined 19% discount, not 20% — a small gap. But two 40% discounts stacked together produce a combined 64% discount, not 80% — a much larger gap. Retailers sometimes use this mismatch to make a combination of offers sound more generous than it mathematically is.

In most U.S. states, sales tax is calculated on the discounted price, not the original sticker price — meaning the discount effectively also reduces the tax owed, not just the item price itself. This is a small detail, but it's worth knowing when comparing a receipt against your own mental math, since a mismatch usually means the discount was applied correctly before tax rather than there being an error.

Occasionally, a promotion is structured differently — for example, a manufacturer rebate applied after the point of sale, rather than a register discount — and in those cases the full pre-rebate price is what gets taxed. It's worth reading the fine print on a promotion to know which type of discount you're actually getting, since the tax treatment can differ.

• Original price — the price before any discount is applied, sometimes called the list price or MSRP.
• Discount rate — the percentage reduction applied to the original price.
• Final price (sale price) — what you actually pay after the discount, before tax.
• Stacked discount — applying two or more discounts one after another, where each one compounds against the already-reduced price rather than adding together.
• Savings — the dollar difference between the original price and the final price.

Start with a straightforward example: a $120 item with a 25% discount.

Now suppose that same $120 item has a storewide 20% discount, and you also have a 10%-off coupon that applies afterward. Here's how the two discounts actually combine:

That 2-percentage-point gap between the "naive" 30% and the real 28% might look small on paper, but on a $1,200 purchase it's the difference between $360 and $336 in savings — a real $24 that a quick mental estimate would have overstated.

To see how sensitive the final price is to the discount percentage, here's the same $120 item at a range of common discount rates:

Notice that at 50% off, savings and final price are exactly equal — a useful mental shortcut: "half off" always means the sale price equals the amount you saved.

• Adding stacked discounts instead of compounding them — 20% off plus 10% off is a combined 28% discount, not 30%, because the second discount applies to an already-reduced price.
• Assuming tax is calculated on the original price — in most places, tax applies to the discounted price, which means the true out-the-door savings on tax are usually a little higher than expected.
• Confusing "percent off" with "percent of" — a 25% discount means you pay 75% of the price, not 25% of it.
• Not checking whether a coupon applies before or after other discounts — the order in which discounts are applied can slightly change the final price when rounding is involved.