Discount Calculator

Multiply the price by the discount percentage to get the savings, then subtract: a $100 item at 25% off saves $25 and costs $75. The faster route skips a step. Multiply by the fraction you still pay — price × (1 − discount) — so 100 × 0.75 = $75 in one operation. That form is worth the small effort of learning, because every other calculation on this page is built from it: 30% off is × 0.70, 40% off is × 0.60, 15% off is × 0.85. Two useful reversals. To find the percent off from two prices, use (original − sale) ÷ original: a $60 item on sale for $45 is 25% off. To recover the original from a sale price, divide by the complement: 45 ÷ 0.75 = $60. People instinctively add the percentage back instead, which is wrong — adding 25% to $45 gives $56.25, not $60.

"20% off, plus an extra 20% at checkout" is not 40% off. It is 36%. The second discount lands on the already reduced price, not the original. $100 at −20% is $80; another −20% takes $16, not $20, leaving $64. In multiplier form the whole thing is one line: 1 − (0.80 × 0.80) = 0.36. Once you see it as multiplication, the pattern generalizes. 25% then 10% is 32.5% off. 30% then 20% is 44%. 50% then 50% is 75% off, not free — that is the extreme case that makes the principle obvious, and it is the same arithmetic as the modest ones. The formula for two stacked discounts is a + b − a × b: the sum, minus the overlap you were double-counting. Stacked offers are always worth less than the headline sum, and the bigger the two discounts, the larger the shortfall.

Raise a price by 10% and then cut it by 10% and you do not return to where you started. 1.10 × 0.90 = 0.99 — you end 1% below the original, and the order does not matter, because multiplication commutes. This is the same asymmetry that makes recovering from a discount harder than granting one. A 50% off sale needs a 100% increase to get back to the original price. A 20% discount needs a 25% increase. In general, undoing a p percent cut takes an increase of p ÷ (100 − p) × 100 percent. It matters on the seller side too. If you discount 30% off list to move inventory, returning to list is a 42.9% price increase, which is a much harder conversation with customers than the discount ever was.

A store discount reduces the pre-tax price, and sales tax is then charged on the reduced amount. So a discount trims the tax along with the price — a nice second-order saving that most people never notice. At an 8% combined rate, a $100 item costs $108 out the door. With 25% off, the taxable price is $75 and the tax is $6, for a $81 total. You saved $25 on the price and $2 on the tax. Manufacturer coupons are the exception worth knowing about, and the treatment varies by state: because the store is reimbursed for the coupon value, some jurisdictions tax the price before the coupon comes off. If the receipt surprises you, that is usually why. To see the full out-the-door number, run the sale price through the sales tax calculator with your local combined rate.

A percentage is only as meaningful as the price it is taken from. "60% off" against a reference price nobody ever paid is a smaller deal than "20% off" against the real going price — the arithmetic is honest, the baseline is what carries the information. Under the FTC's Guides Against Deceptive Pricing, a former price used in advertising is expected to be a genuine, bona fide price at which the item was actually offered for a reasonably substantial period, not an artificial figure set up to be struck through. That is a rule about the seller's claim, not about your math — but it is a good reminder of where to point your skepticism. So the practical habit is to ignore the percentage and compare the final price across sellers, and for consumables to compare price per unit rather than price per package. A 40% discount on a larger box can still lose to an undiscounted smaller one.