Discount Calculator

Background.

Sixty percent off, then an extra 20% off at the register, comes to 68% off, not 80%. The second discount is taken from a price that has already been cut, so it removes less money than its percentage suggests: a $200 jacket drops to $80 after the first markdown, and the extra 20% takes off $16, not $40. Retail signs rely on shoppers adding percentages that actually multiply, and the same sleight of hand turns up in buy-one-get-one offers, in coupon stacks and in sale banners whose "was" price nobody ever paid.

Enter the original price and the percentage off and you get the sale price and the amount you save in dollars. Add your local sales tax rate and you also get the total you will hand over at the register, with tax charged on the discounted price, which is how a store's own markdown is taxed across most of the United States. Leave tax at zero if you only want the pre-tax figure.

The dollar figures often matter more than the percentage. Thirty percent off a $20 item saves $6; ten percent off a $400 item saves $40. When two offers compete, or when a deal means a second trip or a shipping charge, compare what each one saves in cash. A 15% discount on a $40 online order brings it to $34, but with $7.99 shipping the parcel costs $41.99, more than the same $40 item from a shop with free delivery. And before trusting a headline percentage at all, look at the price it is measured from: the Federal Trade Commission's Guides Against Deceptive Pricing say a former price is a fair comparison only if the item was genuinely offered at that price, openly and for a reasonably substantial period.

What is discount calculator?

A percentage discount is a reduction expressed as a share of the original price. At d% off you pay (100 − d)% of the sticker, so 35% off means paying 65 cents of every dollar. The saving is the original price multiplied by d ÷ 100, and the sale price is what remains. Sales tax, when it applies, is then charged as a percentage of that sale price. The percentage is always measured against the original price; measured against the lower price you actually pay, the same saving looks bigger: $25 off $100 is 25% off the original, yet the same $25 is 33.3% of the $75 you paid. Threshold deals work the other way. "$20 off when you spend $100" is a 20% discount only on a basket of exactly $100; spend $130 to qualify comfortably and it is 20 ÷ 130, about 15.4%. Discount should not be confused with markup, the percentage a seller adds to cost, or margin, the share of the selling price that is profit: a $40 item marked up 50% sells for $60 at a 33.3% margin.

How to use this calculator.

1. 01Enter the original price in dollars, as printed on the tag or listing before any markdown.
2. 02Enter the discount as a whole percentage: 40 for "40% off", not 0.40.
3. 03For more than one percentage off, either run the calculator twice, using the first sale price as the second original price, or combine them first: 1 − (1 − a)(1 − b), so 20% then 10% is 28%, and 35% then 10% is 41.5%, which takes a $249.99 tag to $146.24 before tax.
4. 04Enter the combined state and local sales tax rate where you are buying, such as 8.875 in New York City, or leave it at 0 for the pre-tax price or for tax-exempt goods. A recent receipt from the same shop, or your state revenue department's rate lookup, gives the combined figure.
5. 05Read the sale price for the pre-tax cost, the final price for the register total, and the savings in dollars when comparing offers on items with different prices.

The formula.

Three lines of arithmetic: sale price = P × (1 − d ÷ 100); savings = P − sale price; final price = sale price × (1 + t ÷ 100), where P is the original price, d the discount percentage and t the sales tax percentage. Each figure is rounded to the nearest cent. Rearranged, the first line answers the two other questions shoppers ask: the discount behind two known prices is 1 − sale price ÷ P, and the original behind a known sale price is sale price ÷ (1 − d ÷ 100). The effective discount shown with them is the percentage you entered; to see the effective rate of a stacked or multi-buy deal, work out the combined percentage first and enter that.

Because the discount and the tax are both multipliers, the order in which they are applied makes no difference to the total: P × 0.65 × 1.08875 equals P × 1.08875 × 0.65. What does change the total is the base the tax is charged on. If tax were charged on the full sticker price while you paid the discounted one, you would pay tax on money you never spent, and that happens in practice in many states with manufacturer's coupons, which the retailer is reimbursed for. The calculator assumes the common case, a store markdown, taxed on the reduced price.

Stacked percentage discounts multiply: two discounts a and b leave you paying (1 − a)(1 − b) of the price, so 20% and then 20% is 0.8 × 0.8 = 0.64 of the price, a 36% discount rather than 40%. Their order does not matter either. The same multiplication explains why deepening markdowns save more than their headline change: moving from 50% off to 70% off adds 20 percentage points of discount but cuts the price you pay from 0.50 to 0.30 of the original, a 40% fall. A fixed-dollar coupon is different: it does not scale with the price, so whether it comes before or after a percentage changes what you pay, and a coupon deducted before tax is worth its face value plus the tax on it, C × t more than the same coupon deducted after tax.

A worked example.

Frequently asked questions.

References& sources.

1. [1]16 CFR Part 233 — Guides Against Deceptive Pricing, § 233.1 Former price comparisons. Federal Trade Commission. The authoritative federal rule for when an advertised 'was/now' or 'X% off' claim is lawful and when it is deceptive.
2. [2]U.S. Internal Revenue Service, Publication 535 — Business Expenses, on the treatment of trade discounts and the basis for sales tax computation in retail transactions.
3. [3]Tan, P. J. & Bogomolova, S. (2016). A descriptive analysis of consumer's price promotion literacy skills. International Journal of Retail & Distribution Management, 44(12). Peer-reviewed evidence that consumers systematically overestimate the value of percentage-off promotions versus equivalent dollar-off promotions.
4. [4]Guha, A., Biswas, A., Grewal, D. & Verma, S. (2018). Reframing the discount as a comparison against the sale price: does it make the discount more attractive? Journal of Marketing Research, 55(3). Documents how the framing of a percentage discount changes consumer evaluation of the offer.
5. [5]Federation of Tax Administrators (FTA), State Sales Tax Rate Tables. Authoritative source for combined state and local sales tax rates used to test the post-discount tax calculation.
6. [6]U.S. Bureau of Labor Statistics, Consumer Expenditure Survey — Section on retail discounting behavior. Background data on how often U.S. households purchase at full price versus on promotion.