Black Friday, one jacket, one tag: was $869, now 35 percent off. Two numbers matter and shoppers constantly grab the wrong one. The discount amount is 869 times 0.35, which is $304.15 — that is what you save. The sale price is 869 minus 304.15, which is $564.85 — that is what you pay. Every discount problem is some version of those two numbers, and this page walks through all of them: forward, backward, stacked, bundled, and taxed.

The two numbers every discount gives you.

A discount always hands you two figures, and keeping them straight is half the skill. The amount you save is the original price times the discount rate. The price you pay is the original price minus the savings. On the calculator's first example, 20 percent off $85: the savings are 85 times 0.20, which is $17, and the sale price is 85 minus 17, which is $68. The second example is cleaner still: 50 percent off $200 saves $100 and leaves a $100 sale price. The third example shows why small percentages still matter on big tickets: 5 percent off $1,500 saves $75 and leaves $1,425. A 5 percent early-pay discount on a $1,500 appliance is a free dinner out, and most people walk past it because the percentage looks small.

The one-step shortcut.

You can skip the subtraction entirely. The sale price is the original price times one minus the discount rate. Thirty-five percent off means you pay 65 percent, so 869 times 0.65 is $564.85 in one step. Twenty-five percent off $45 jeans: 45 times 0.75 is $33.75, no subtraction needed. Five percent off $1,500: 1,500 times 0.95 is $1,425. This shortcut is also the fastest way to sanity-check a store tag. If the shelf says 30 percent off $80 and the register shows $60, something is off: 80 times 0.70 is $56, not $60. The register either applied 25 percent or the tag lied, and now you know which question to ask.

Working backwards: finding the original price.

Sale tags show the price you pay and hide the price you saved from, but the math runs in reverse just as cleanly. Divide the sale price by one minus the discount rate. Jeans ring up at $33.75 after 25 percent off, so the original was 33.75 divided by 0.75, which is $45. A jacket at $68 after 20 percent off was originally 68 divided by 0.80, which is $85. A blender at $56 after 30 percent off started at 56 divided by 0.70, which is $80. This reverse move is the one that exposes inflated was-prices: if a store claims a $120 item was $200, check it. The claimed discount is 80 dollars on a 200-dollar original, which is 40 percent — plausible. But if the same $120 item claims a was-price of $240, the discount would be 50 percent, and if you have never seen that item above $150 anywhere, the was-price is marketing, not history.

Working backwards the other way: finding the discount percent.

Sometimes you have both prices and want the percentage, which is how you compare deals honestly. Subtract the sale price from the original, divide by the original, and multiply by 100. A coat marked down from $129 to $103.20: the cut is $25.80, and 25.80 divided by 129 is 0.20, so 20 percent off. A speaker dropping from $120 to $90: the cut is $30, and 30 divided by 120 is 0.25, so 25 percent off. The critical detail is the denominator: always divide by the original price. Dividing by the sale price inflates every discount — that same $30 cut divided by $90 gives 33 percent, which is fantasy. Stores that quote discounts measured from the sale price are either sloppy or dishonest, and now you can tell.

Stacked discounts multiply, they never add.

This is the trap that catches even careful shoppers. Twenty percent off, then another 10 percent off, is not 30 percent off. The first cut takes a $120 item to $96; the second takes 10 percent of $96, which is $9.60, leaving $86.40. You saved $33.60 on $120, which is 28 percent, not 30. On a $100 item the same pair gives $80 then $72 — again 28 percent. The order does not matter: 0.80 times 0.90 is 0.72 either way, and 0.90 times 0.80 is also 0.72. The general rule is that stacked discounts multiply the keep-fractions: for rates r1 and r2, you pay (1 minus r1) times (1 minus r2) of the original. Two 50-percent cuts do not make the item free; they leave you paying 25 percent, a 75 percent total discount. Coupon stacking works the same way, and it is why a 20-percent coupon on top of a 40-percent sale saves 52 percent, not 60: 0.60 times 0.80 is 0.48, so you pay 48 percent.

Bundle deals in percent terms.

Buy-one-get-one-free, three-for-two, and four-for-three are discounts wearing costumes, and converting them to percentages makes them comparable. Buy one get one free means you pay for one item and take two, so each item costs half price: 50 percent off per unit. Three for two means you pay for two and take three, so each costs two-thirds: about 33.3 percent off. Four for three means each costs three-quarters: 25 percent off. Now a straight percent offer can be judged against them. A $15-off coupon on a $70 item is 15 divided by 70, which is 21.4 percent — worse than a 3-for-2 deal on the same item, and worse than a straight 25 percent off $80, which saves $20. Comparing dollar savings across different prices misleads; comparing percentages does not. A $40 saving on a $400 television (10 percent) is a worse deal than a $30 saving on a $120 speaker (25 percent), even though $40 looks bigger.

Sales tax comes after the discount, almost always.

In most US states, sales tax is charged on the discounted price, not the original — so a discount lowers the tax you owe as well as the price. A $68 sale price at a 6 percent tax rate costs 68 times 1.06, which is $72.08 at checkout. At an 8 percent rate it would be $73.44. The exception worth knowing: a few states treat manufacturer coupons differently from store discounts and tax the pre-coupon price, so a coupon deal can ring up a few cents higher than the simple math predicts. If your receipt looks wrong by a small amount, check whether the coupon was a manufacturer coupon before assuming the store erred. And remember the calculator shows the pre-tax sale price, because tax rates vary by state and county — add your local rate to the sale price for the register total.

Mental math at the shelf.

You do not need the calculator for round numbers if you anchor on 10 percent. Ten percent of any price is the price with the decimal moved one place left: 10 percent of $85 is $8.50. Twenty percent is double that, $17. Thirty percent is triple, $25.50. Fifteen percent is 10 percent plus half of 10 percent: $8.50 plus $4.25 is $12.75. Twenty-five percent is a quarter: divide by 4. Five percent is half of 10 percent. For awkward prices, round first and correct: 15 percent off $19.99 is about 15 percent off $20, which is $3.00, leaving $17.00; the exact math gives 19.99 times 0.85, which is $16.99, saving $3.00 — the rounding cost you one cent. That one-cent gap is also why register totals sometimes differ from your mental math by a penny: stores round the final price to the nearest cent, and the savings figure absorbs the fraction.

Spotting a fake discount.

A discount is only real if the original price was real. Watch for three tells. First, a was-price you have never seen the item sell at — the $240 was-price on a $120 item nobody ever bought above $150. Second, a discount that only exists in the ad: the shelf tag says 40 percent off but the register applies it to a different, higher base price. Third, the shrinking-product trick: the price drops 20 percent but the box drops from 16 ounces to 12, which is a 25 percent quantity cut hiding inside a price cut. The defense is always the same arithmetic: cut divided by original, times 100. If the store will not show you a genuine original price, treat the discount claim as advertising, not information.

The business side: markup versus margin.

Shoppers are not the only ones doing discount math. A retailer who buys an item for $40 and sells it at $68 after discount is working with two different percentages. Markup is profit divided by cost: 28 dollars of profit on a 40-dollar cost is 70 percent markup. Margin is profit divided by sale price: 28 dollars on a 68-dollar sale is 41.2 percent margin. Confusing them is how small sellers lose money: a 40-percent markup is not a 40-percent margin, and pricing a sale from the wrong one quietly erases the profit the sale was supposed to protect. If you ever sell on a marketplace, learn margin first — it is the number that tells you whether the sale was worth running.

One more quiet trap: a discount that applies to only part of the cart. A 20-percent coupon marked for a single item does not discount the whole basket, and a free-shipping threshold counts the post-discount subtotal, not the pre-discount one. A $52 cart with a 20-percent coupon on a $30 item drops by $6, not by $10.40, and if the store's free-shipping line is $50, that $46 post-discount subtotal may suddenly owe shipping. Read the coupon's scope before assuming the whole cart shrinks.

Mistakes that cost real money.

The classics, in one place: confusing the discount amount with the sale price (saving $304 is not paying $304); adding stacked discounts instead of multiplying them; dividing by the sale price instead of the original when finding a percent; comparing dollar savings across different prices instead of percentages; forgetting tax until the register; and assuming a discount makes an unneeded purchase a good deal. That last one is the most expensive mistake on this page. A 70-percent discount on something you would never buy at full price is not saving 70 percent — it is spending 30 percent of a price on something worth zero to you. The calculator tells you the price. Only you can tell whether the item is worth it.

Down, then up, is not back to even.

A related asymmetry catches shoppers who watch prices bounce. Take 25 percent off an $80 item, then 25 percent back up: the cut takes it to $60, and the increase takes $60 to $75 — still $5 short of $80. The percentages look equal but their bases differ: the cut applies to $80, the increase to $60. To undo a 20 percent cut you need a 25 percent increase, because 80 times 1.25 is 100. To undo a 25 percent cut you need a 33.3 percent increase, because 75 times 1.3333 is 100. This is why a stock that falls 50 percent must rise 100 percent to break even, and why a sale price that later returns to its original tag has risen by a larger percentage than the discount that lowered it. Percent changes are not reversible unless you change the base, and retailers quietly rely on shoppers not noticing.

When a discount is not a deal.

Two final checks before any sale purchase. First, the per-unit check: a bulk price that looks discounted can cost more per ounce than the smaller size — divide price by quantity on both sizes before choosing. Second, the calendar check: big-ticket categories have predictable sale seasons — televisions before the Super Bowl and on Black Friday, mattresses around Presidents Day and Memorial Day, outdoor gear at end of summer. A 20-percent discount today can be a 40-percent discount in six weeks, and patience is the only coupon that never expires. Use the calculator to price the deal in front of you, then decide whether the deal in front of you is the one worth taking.

With the pre-filled defaults — Original Price $100, Discount 20% — the Discount Calculator returns Sale Price $80.00, You Save $20.00, You Pay 80.0%. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.