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Take 20% off a $100 item and then 20% off again and you pay $64.00, because the two discounts multiply rather than add: together they are 36% off, not 40%. Whether the discount also cuts the sales tax turns on something the sticker does not say, which is who reimburses the shop. And the FTC has a published standard for what the higher price is allowed to be.
Last updated 1 October 2026
Arithmetic and sourced rules, not legal or tax advice. The figures above come from the three numbers you type. The Tax field applies its rate to the discounted price. Whether that is the right order for a particular purchase is a question of state law and of who is funding the discount, and the published rules on both are quoted and cited below.
Not 40%. The second discount is taken on the reduced price, so the two do not add, they multiply. Twenty per cent off leaves 80% of the price; 20% off that leaves 80% of 80%, which is 64%. On a $100 item the till reads $64.00, and a shopper who did the mental arithmetic as 40% is $4.00 out.
The general form is short enough to memorise: what you pay is the product of what each discount leaves, so the single equivalent discount is one minus that product.
Stacked discounts and the single discount that matches them
Put a real price on the third row, because that is the one the signs in a shop window usually describe. A $59.99 jacket at 30% off, with a coupon for an extra 20% off at the till, comes to $33.59. Fifty per cent off the same jacket would be $30.00. The gap is $3.59, which is to say the stacked offer that reads as the bigger one is the smaller one.
Two useful corollaries. Stacking is order-independent while every discount is a percentage, because multiplication is. It stops being order-independent the moment one of them is a fixed amount: on a $100 item, $10 off and then 20% off is $72.00, while 20% off and then $10 off is $70.00. If the terms let you pick, apply the fixed amount last. And a percentage never undoes itself. A $100 item marked up 20% is $120, and 20% off $120 is $96.00, not $100, because the second percentage works on a bigger base than the first.
The field above takes one discount. Where an offer stacks, run it twice, or enter the single equivalent from the table.
A fixed amount is a shrinking discount as the price rises, and a percentage is a growing one, so they cross exactly once. They are level where the coupon equals that percentage of the price, which makes the break-even price the coupon divided by the rate.
$10 off against 20% off
So the rule of thumb is a single division. A $25 coupon is worth more than 15% off anything under $166.67 and less than it above. When a shop offers you a choice of the two, you are being asked to do that division at the counter.
A discount is a claim about two prices, and the second one is the one with a federal standard attached. The Federal Trade Commission’s Guides Against Deceptive Pricing, issued under sections 5 and 6 of the FTC Act and published at 32 FR 15534 on 8 November 1967, open on exactly this:
“If the former price is the actual, bona fide price at which the article was offered to the public on a regular basis for a reasonably substantial period of time, it provides a legitimate basis for the advertising of a price comparison. Where the former price is genuine, the bargain being advertised is a true one. If, on the other hand, the former price being advertised is not bona fide but fictitious—for example, where an artificial, inflated price was established for the purpose of enabling the subsequent offer of a large reduction—the ‘bargain’ being advertised is a false one.”
Two refinements in the same section are worth knowing, because they cut in opposite directions. A former price is “not necessarily fictitious merely because no sales at the advertised price were made”, so an item that nobody bought at full price can still be honestly marked down. But the advertiser “should scrupulously avoid any implication that a former price is a selling, not an asking price (for example, by use of such language as, ‘Formerly sold at $______’), unless substantial sales at that price were actually made.”
The Guides then do something regulations rarely do and work an example, in their own numbers:
“John Doe is a retailer of Brand X fountain pens, which cost him $5 each. His usual markup is 50 percent over cost; that is, his regular retail price is $7.50. In order subsequently to offer an unusual ‘bargain’, Doe begins offering Brand X at $10 per pen. He realizes that he will be able to sell no, or very few, pens at this inflated price. But he doesn’t care, for he maintains that price for only a few days. Then he ‘cuts’ the price to its usual level—$7.50—and advertises: ‘Terrific Bargain: X Pens, Were $10, Now Only $7.50!’”
16 CFR 233.1(c). Enter $10 and 25% above and you get $7.50, which is the point: the arithmetic is impeccable and the offer is not.
Section 233.4 covers the family of offers that look like discounts without being priced as one, and it names them: “Free,” “Buy One—Get One Free,” “2-For-1 Sale,” “Half Price Sale,” “1¢ Sale,” “50% Off”. Its concern is the hidden adjustment: where a seller “increases his regular price of the article required to be bought, or decreases the quantity and quality of that article, or otherwise attaches strings”, the consumer may be deceived, and so “all the terms and conditions of the offer should be made clear at the outset.” Which settles the buy-one-get-one question arithmetically too: it is 50% off the pair, and this page will tell you so if you enter 50 and read the result as the cost of two.
Section 233.5 sweeps up the rest in a list that reads like a tour of a clearance aisle. Retailers “should not advertise a retail price as a ‘wholesale’ price”, should not claim “‘factory’ prices when they are not selling at the prices paid by those purchasing directly from the manufacturer”, should not offer “seconds or imperfect or irregular merchandise at a reduced price without disclosing that the higher comparative price refers to the price of the merchandise if perfect”, and should not “make a ‘limited’ offer which, in fact, is not limited.”
These are Guides rather than a statute, which matters for how they bite: they state the Commission’s view of what section 5 forbids, and they are the document an enforcement action reasons from. Nothing in them tells you a particular sale is genuine. What they give a shopper is a precise idea of what question to ask, which is how long the higher price was actually the price.
This is the part no discount calculator mentions, and it moves real money. The Tax field above charges tax on the discounted price. For a discount the shop is absorbing, that is right. For a manufacturer’s coupon, published state guidance says it is wrong, and the reason is that the shop is not actually receiving less.
New York states both halves in one bulletin. On a store coupon: “since the seller will not be reimbursed for the amount of the coupon, the actual amount received is reduced, and tax is calculated on the reduced price.” On a manufacturer’s coupon: “when a customer uses a manufacturer’s coupon, sales tax is due on the full price of the item, not on the discounted price”, because “the seller will receive reimbursement from the manufacturer for the amount of the coupon, the actual selling price is not reduced.” California reaches the same place from the seller’s side: “amounts paid by manufacturers to reimburse you for the value of the manufacturer’s coupons are included in your total taxable sales when the sale is subject to tax.”
New York works it on a $1.00 item with a 25 cent coupon at 8%. The two answers are 81 cents and 83 cents. Two cents is easy to dismiss, so here is the same rule on a purchase worth noticing, at an illustrative 8.25% rate:
A $40 item, a $10 coupon, a rate of 8.25%
The tax on $30.00 there is exactly $2.475, and it becomes $2.48 rather than $2.47 under the rounding algorithm several states impose: Florida requires that “the computation of the tax must be carried to the third decimal place; if the third decimal place is greater than 4, the tax must be rounded up to the next cent”, and Section 324 of the Streamlined Sales and Use Tax Agreement requires the same of its member states.
A rebate is a third case again, and the giveaway is the timing. A discount changes the price at the till; a rebate pays you back after a sale that already happened at the full price. If you are reaching for this page to compare a rebate against a discount, compare them after tax, not before.
A price, one discount and one tax rate: that is the whole input. The honest part of a page like this is being exact about the questions those three figures do not even pose.
Whether the higher price was ever the price. The original-price field accepts whatever you type. The FTC’s standard for that figure is a bona fide price “offered to the public on a regular basis for a reasonably substantial period of time”, and no calculator can audit it. The arithmetic is equally correct on a genuine markdown and on John Doe’s fountain pens.
Who is reimbursing the seller. It decides the taxable base, as above, and it is nowhere in the three numbers. A manufacturer’s coupon and a store sale of identical face value produce different totals.
Your rate, and what it applies to. A rate belongs to an address, and in many states groceries, medicine and clothing under a threshold are taxed differently or not at all. One rate over a mixed basket is one rate over the wrong base.
A second discount, a minimum spend, an excluded brand, an expiry. One discount field is one discount. Stacking, thresholds, exclusions and end dates are terms, and the Guides ask that they be “made clear at the outset” rather than computed.
Shipping, a membership fee, or the cost of getting to the shop. None of them is an input, and a free-shipping threshold is the most common reason a smaller discount wins.
Whether the thing is worth buying. A per cent off is a statement about a price, not about value. Nothing here recommends a purchase.
Boundary behaviour worth knowing. A negative price, discount or tax rate is raised to zero and a discount or tax rate above 100% is lowered to 100%, and in each case the field is rewritten to the figure actually used when you leave it. The price is capped at $1 trillion, which is where whole cents stop being exact arithmetic here.
Nothing you type into the fields above leaves your browser.
Every quotation above was read from the document named on 1 October 2026. Each dollar figure in the tables was computed by hand in exact decimal arithmetic before being written, and the rounding rule quoted above was applied where a figure landed on a half cent. Part of the QuikUtil tools collection; the Sales Tax Calculator goes into how a rate is assembled from a state, a county and a city, and the Percentage Calculator handles the reverse question of what per cent one figure is of another.
No. They multiply. Twenty per cent off leaves 80% of the price, and 20% off that leaves 80% of 80%, which is 64%, so the two together are 36% off. On a $100 item the sale price is $64.00 and not $60.00. The general form is one minus the product of what each discount leaves: 30% and then 20% is 44% off rather than 50%, and three successive 10% discounts come to 27.1% off rather than 30%.
Not when both are percentages, and very much when one is a fixed amount. Two percentages multiply, and multiplication does not care about order. A dollar amount does. On a $100 item, taking $10 off and then 20% off gives $72.00, while taking 20% off and then $10 off gives $70.00. If the terms let you choose, take the fixed amount off last.
Below $50 it is, above $50 it is not, and at exactly $50 they are identical. The two are equal where the fixed amount equals the percentage of the price, so the break-even price is the coupon divided by the rate: $10 divided by 0.20 is $50. The same arithmetic puts a $25 coupon level with 15% off at a price of $166.67.
It depends on who ends up paying for the discount, and the rule is published. New York’s guidance on a store coupon: “since the seller will not be reimbursed for the amount of the coupon, the actual amount received is reduced, and tax is calculated on the reduced price.” On a manufacturer’s coupon the opposite: “when a customer uses a manufacturer’s coupon, sales tax is due on the full price of the item, not on the discounted price”, because “the seller will receive reimbursement from the manufacturer for the amount of the coupon”. California says the same of the reimbursement: “amounts paid by manufacturers to reimburse you for the value of the manufacturer’s coupons are included in your total taxable sales when the sale is subject to tax.” The Tax field above applies the rate to the discounted price, which is the store-discount case.
On New York’s own worked example, a $1.00 item with a 25 cent coupon at 8%, a store coupon leaves the customer paying $0.81 and a manufacturer’s coupon $0.83. Scale it up and it stops being trivia: a $40 item with a $10 coupon, at an illustrative 8.25%, costs $32.48 when the discount is the store’s and $33.30 when the coupon is the manufacturer’s. That is 82 cents on the same two dollar figures, decided entirely by who sends the seller a cheque afterwards.
No, and the standard is federal. The FTC’s Guides Against Deceptive Pricing require that “the former price is the actual, bona fide price at which the article was offered to the public on a regular basis for a reasonably substantial period of time”. A price invented to be marked down is named in the Guides as the thing they exist to stop: “where an artificial, inflated price was established for the purpose of enabling the subsequent offer of a large reduction”, the bargain “is a false one”. No sales at the higher price need ever have happened, but the advertiser must not imply they did “unless substantial sales at that price were actually made.”
On the pair, yes, and the FTC Guides list the two phrases side by side for that reason, along with “2-For-1 Sale”, “Half Price Sale” and “1¢ Sale”. The Guides also name the way such an offer goes wrong: if the seller “increases his regular price of the article required to be bought, or decreases the quantity and quality of that article”, the consumer may be deceived. Their requirement is that “all the terms and conditions of the offer should be made clear at the outset.” Enter 50% above to price the pair; it is not 50% off one item.
It lands 4% below it. A $100 item marked up 20% is $120, and 20% off $120 is $96.00, because the second percentage is taken on a larger base than the first was. The same asymmetry is why a 50% fall needs a 100% rise to recover.