Article — Percent Off Calculator
Percent Off: How Discounts Actually Work
To calculate a percent off, multiply the price by 1 minus the discount as a decimal. A $80 item at 25% off costs $80 × 0.75 = $60. For stacked discounts ("20% off, then extra 10%"), apply each layer to the price that remains after the previous one — the layers multiply rather than add. Two 50% discounts in a row give 75% off, not 100%.
The math is simple. The retail psychology around it is not, which is why most people get stacking wrong, why sales tax handling varies by state, and why "original prices" on sale tags are sometimes legally suspect. The sections below cover the calculations first, then the consumer-protection rules and the psychology that drives how stores price their sales.
A single percent off: the basic case
A 20% discount means the buyer pays 80% of the listed price. Multiply the price by 0.80 and you have the new price; multiply by 0.20 and you have the savings. The two routes give the same answer, and the calculator does both at once.
The most-asked single-discount questions on the Internet, all worked out:
$50 at 20% off = $40 (save $10)$100 at 25% off = $75 (save $25)$200 at 30% off = $140 (save $60)$50 at 40% off = $30 (save $20)$100 at 75% off = $25 (save $75)Stacking discounts: why 20 plus 10 is not 30
Coupon stacks are the source of more arithmetic errors than any other percent-off problem. The natural reading of "20% off, then extra 10% off with code SAVE10" is that the buyer gets 30% off the original price. The actual math is different.
The second discount applies to the price after the first one, not to the original. So a $100 item at 20% off first becomes $80; then the extra 10% off the $80 takes another $8, leaving $72. The buyer paid 72% of the original price, which is a 28% effective discount, not 30%.
The general rule for stacking: multiply the "keep" fractions. A 20% off plus 10% off becomes 0.80 × 0.90 = 0.72. The final price is 0.72 × original; the effective discount is 28%.
"Buy one, get one 50% off" is not the same as 50% off two items. The first item is full price; the second is half price; the average per item is 75% of full price, not 50%. The effective discount across the two items is 25%, not 50%. Always compute the actual total before celebrating the headline number.
Tax: before or after the discount?
In most US states, sales tax is charged on the discounted price, not the original. The order at checkout is: list price, minus all discounts and store coupons, equals taxable amount; then tax is added. A $100 item with a 20% off promo and 8% sales tax becomes $80 + $6.40 = $86.40.
The exception is manufacturer coupons in a few states. New York, California, and several others sometimes treat a manufacturer coupon (which the retailer is reimbursed for) as part of the price for tax purposes, meaning tax is calculated on the pre-coupon amount. Store-issued coupons are uniformly taxed on the discounted price.
Five US states have no state sales tax: Alaska (mostly, with local exceptions), Delaware, Montana, New Hampshire, and Oregon. The remaining 45 states charge 2.9% (Colorado) to 7.25% (California) at the state level, with local rates often adding several more percentage points. Chicago tops out at 10.25%.
- Order matters — discount first, then tax
- Store coupons always reduce the taxable amount
- Manufacturer coupons may or may not, depending on the state
- Restaurant tip conventionally calculated on pre-tax price
- Gift cards not taxed when purchased, taxed when redeemed
- No-tax states Oregon, Montana, New Hampshire, Delaware, parts of Alaska
Fake discounts and the inflated MSRP
Not every "$199 — was $399" tag means what it appears to mean. The Federal Trade Commission's Guides Against Deceptive Pricing (16 CFR Part 233) prohibit retailers from comparing a current price to a "former" price that was not actually a recent, regular price. State attorneys general enforce parallel rules; California's "ARPA-style" pricing laws are among the strictest.
The standard workaround is to compare against the manufacturer's suggested retail price, or MSRP. The MSRP is set by the maker, not the seller, and may have been used briefly at a flagship store or premium outlet. As long as some retailer charged that price, the comparison is technically defensible. The Federal Trade Commission has guidance specifically warning against this when the MSRP was never the seller's own price.
The Consumer Financial Protection Bureau and several state regulators have written about a related problem: "drip pricing," where the headline price is real but fees and surcharges added at checkout substantially raise the total. The FTC's June 2024 rule against hidden fees in the hotel and event-ticket industries addresses this directly.
The FTC's deceptive-pricing guidance has been on the books since 1964. The key language: "Where former price comparisons are based upon a fictitious mark-up... they will of course be deceptive." Enforcement has accelerated in the past decade as e-commerce makes "was $X" comparisons trivially easy to display. Major retailers settled multimillion-dollar cases on this point with the attorneys general of California, Colorado, and New York between 2014 and 2023.
Anchoring: why the original price is on the tag
In 1974, Daniel Kahneman and Amos Tversky published a study in Science showing that people's numeric judgments are pulled toward whatever number they happen to see first, even when that number is obviously irrelevant. Participants who spun a wheel that landed on 65 estimated that 45% of African countries were UN members; participants who got 10 estimated 25%. The wheel was a random anchor; the effect was reliable across hundreds of replications.
Retail tags are anchors. Showing "$399, now $199" makes the $199 feel like a deal, regardless of what the product is worth or what anyone else charges for it. The discount sign and the strike-through on the original price are both deliberate signals that the lower number is a deal. Kahneman won the 2002 Nobel Prize in Economics for this and related work on judgment under uncertainty.
Mental shortcuts for common discounts
Some percent-off numbers are easier to do in your head than others. 10% is a decimal shift: $137 at 10% off is $137 - $13.70 = $123.30. 25% is a quarter: $80 at 25% off is $80 - $20 = $60. 50% is half: $90 at 50% off is $45. These three cover most checkout situations.
For trickier numbers, decompose the discount. 30% off is 10% off three times — calculate 10% (move the decimal), multiply by 3, subtract from the original. 40% off is 10% off four times. 75% off is half off twice. 15% off is 10% off plus half of that.
If a tag says "additional 30% off lowest ticketed price," the lowest ticketed price is usually after the first discount, not the original. So the math is: original × (1 - first discount) × 0.70. The second 30% sounds bigger than it is. Always check what the "lowest ticketed price" refers to before celebrating.
Discount versus markup: not the same thing
A discount reduces a price; a markup raises a cost. The two are computed from different starting points. A 50% markup on a $40 cost gives a $60 sale price ($40 + $20). A 50% discount on a $60 sale price gives a $30 final price ($60 × 0.50). They are not inverse operations: a 50% markup is not undone by a 50% discount.
This trips up small retailers and is sometimes weaponized in sales pitches. "Take 30% off our 30% markup" sounds like a wash but is not. A $100 cost with 30% markup is $130; 30% off $130 is $91. The retailer takes a $9 loss per item.