Article — Discount Calculator (% or $ Off + Tax)
Discount calculator: percent off, dollar off, and what stores cannot do
A discount is a reduction from a stated original price. To calculate a discount, multiply the original price by the discount percentage (as a decimal) and subtract from the original. So 25% off $80 = $20 saved, $60 final. The formula is F = P x (1 - d/100). When sales tax applies, the US standard is to compute it on the discounted price — not the original.
The simple formula hides a few traps. Stacked discounts multiply rather than add (20% off plus 10% off equals 28% off, not 30%). MSRPs can be inflated to make the discount look bigger than it is. And the FTC regulates what stores can legally call an "original price."
What is a discount?
A discount is a temporary price reduction below an item's normal selling price. Retailers use the word loosely to mean any price cut: a coupon code, a member discount, a store-wide sale, an end-of-season markdown, a clearance tag. Mathematically all of these reduce a starting price to a final price using one of two formats: a percentage (25% off) or a dollar amount ($20 off).
The English word comes from medieval Latin "discomputare" — to deduct from a count. The modern retail meaning has been in English since the late 1700s, originally meaning "deduction from the face value of a bill." Banking still uses "discount" in the original sense (discounting a future cash flow to present value), but retail uses the word to mean a percent-off-now offer.
The first US department store, Wanamaker's in Philadelphia, introduced the concept of a fixed, posted price in 1876. Before that, customers haggled with each clerk individually. The fixed-price revolution made percentage discounts meaningful for the first time — you could now compare 20% off at Wanamaker's against 10% off at a competitor, because both stores had a number on the tag.
How to calculate a discount (percent and dollar)
For percentage discounts the formula is F = P x (1 - d/100), where P is the original price, d is the discount percent, and F is the final price. The savings (the amount you do not have to pay) is P - F, which also equals P x d/100. For 25% off $80: F = $80 x (1 - 0.25) = $80 x 0.75 = $60. Savings: $80 - $60 = $20.
For dollar-off discounts the math is simpler: F = P - D, where D is the discount amount. The implied percent off is D / P x 100. A $20 discount on an $80 item: F = $80 - $20 = $60. Implied percent: 20/80 x 100 = 25%.
10% off: move decimal one place left25% off: divide by 433% off: divide by 350% off: halve itThe reverse calculation is also useful. If you know what you paid and what the sticker said, you can find the discount percent: d = (P - F) / P x 100. Paid $60 for an $80 item: (80 - 60) / 80 x 100 = 25%. To work back from a final price to the original (e.g., to verify the store's math), divide the final price by (1 - d/100). $60 with 25% off implies an original of $60 / 0.75 = $80.
Common discount amounts in retail
Retail discount levels cluster at a few round numbers. The reasons are partly psychological and partly historical, but they show up consistently in US shelf data.
- 10% off: standard welcome offer (newsletter signup, first-time buyer)
- 15% off: typical loyalty-program rate
- 20% off: anchoring number for "sale" pricing
- 25% off: clean quarter discount, common at department stores
- 30% off: aggressive seasonal sale
- 40% off: end-of-season markdown
- 50% off: half off; signals clearance or BOGO
- 75% off: deep clearance, signal of stock liquidation
The 99-cent price ending (the "left-digit effect") works similarly — $19.99 reads as "ten-something" to the brain even though it rounds to $20. Discounts use the same trick: "30% off" feels meaningfully bigger than "29% off" because the leading digit drops from 3 to 2 when you compute. Walmart and Costco data shows 30% and 40% are the two most-advertised levels, far ahead of 28% or 32%.
Discount with sales tax (order matters)
In the United States, sales tax is calculated on the discounted price in almost every state. The order is: subtract the discount first, apply tax second. For an $80 item with 25% off and 8% sales tax: $80 x 0.75 = $60, then $60 x 1.08 = $64.80. The tax savings from the discount: ($80 - $60) x 0.08 = $1.60. That is part of why a 25% sale feels like more than 25% — you also save tax on the difference.
Five US states have no state sales tax: Oregon, Montana, New Hampshire, Delaware, and Alaska. In those states the discount-then-tax order is moot. Combined state-and-local rates in the rest of the country range from about 4% (Hawaii) to over 10% (Chicago, Birmingham AL). The Tax Foundation publishes the annual rankings, with Tennessee and Louisiana usually at the top of combined averages.
Two states (Illinois and Connecticut) require sales tax to be calculated on the pre-coupon price when the coupon comes from a manufacturer (not the store). The retailer is reimbursed by the manufacturer for the coupon amount, so from the state's perspective the buyer is paying full price — the discount is just routed through a third party. Store coupons (from the retailer itself) are universally taxed on the post-coupon price.
MSRP versus sale price (and FTC rules)
MSRP stands for Manufacturer's Suggested Retail Price. It is a number the manufacturer publishes as a reference price. Retailers can choose to sell at MSRP, above MSRP, or below MSRP — the suggestion is not binding. In categories like consumer electronics and toys, real selling prices have drifted so far below MSRP that the suggested price functions mainly as a reference point for advertising discounts.
The "discount from MSRP" framing has been controversial since the 1980s. If Sony lists a TV at $999 MSRP but no store ever sells at that price (Best Buy lists at $799, Walmart at $749), advertising "$200 off MSRP" misrepresents the savings. The buyer is not actually getting a $200 discount — they are getting the normal market price, and the $200 figure is a marketing construct.
Fake discounts and the FTC deceptive-pricing rule
The Federal Trade Commission regulates discount advertising through the Guides Against Deceptive Pricing, codified as 16 CFR Part 233. The rule is short and direct: an advertised "former price" must be the price at which an article was "openly and actively offered for sale" for a reasonably substantial period of time. Inflating a former price to make the discount look bigger is, in FTC terms, an "unfair or deceptive act or practice."
The rule has been the basis for several large class-action settlements. In 2016, JCPenney paid $50 million to settle claims that it had systematically inflated original prices so that the perpetual sale price looked like a meaningful discount. The court found that the products had not actually sold at the supposed original price, which made the percent-off claims deceptive. Kohl's, Macy's, Sears, and JoS A Bank have faced similar suits with various outcomes.
The rule applies to MSRPs too. If the manufacturer's suggested price is fictional — the manufacturer never sold or expected anyone to sell at that price — advertising "X% off MSRP" can be deceptive even if the MSRP itself is technically a manufacturer document. The FTC has gone after several outlet-mall chains for using "Compare At" prices that were not real market prices.
Camelcamelcamel (for Amazon) and Honey track historical prices on individual SKUs. When a retailer advertises 40% off, you can verify whether the "original" was ever real by checking the price history. If the SKU has been at the sale price for months and the only time it touched the "original" was for a few days a year ago, the discount is technically real but practically misleading.
Common discount-calculation mistakes
Stacking is the leading source of error. "An extra 20% off our already 30% off prices" does not equal 50% off. The math: 0.70 x 0.80 = 0.56, so the effective discount is 44%. The two discounts multiply because the second one applies to the already-reduced price. To get a true 50% off you need the math to work out to 0.50, which means the two stacked percentages would have to satisfy (1 - d1) x (1 - d2) = 0.50.
Ignoring tax is the second leading error. A buyer who calculates "$80 minus 25% equals $60" and brings $60 to the register will be short. The full out-the-door price in an 8% sales tax jurisdiction is $64.80. Tax on the discount — the tax savings — is a real number ($1.60 in this example) but a smaller number than the discount itself.
The third error is treating "buy one get one free" (BOGO) as a flat 50% off. BOGO is only 50% off if you buy exactly two units. Buy one unit and you get 0% off (no second item to discount). Buy three units and you get 33% off (pay full for two, get one free). The discount percentage depends on the quantity.