How to Calculate a Sale Discount: Formulas, Examples, and Common Traps

Original price minus discount equals what you pay. Then retailers stack percentages, add coupons, choose when to apply tax, and pick which "original" to print on the tag, and the sign on the rack stops matching the receipt.

All of it comes from one formula and four places people get the order wrong.

The formula everything else is built from

sale price      = original * (1 - discount)
discount amount = original * discount

An 80 jacket at 25 percent off is 80 x 0.75 = 60, and the saving is 80 x 0.25 = 20.

The Discount Calculator applies it directly, and the percentage calculator handles the inverse cases, like working backwards from a sale price to the rate.

Stacked discounts never add

"25 percent off, then an extra 20 percent" is not 45 percent. The second rate applies to what is left after the first.

On a 100 item: 100 x 0.75 = 75, then 75 x 0.80 = 60. That is 40 off, so 40 percent.

combined factor   = (1 - a) x (1 - b)
combined discount = 1 - combined factor

For any number of stacked rates, multiply all the leftovers together. The result is always less than the sum, and the shortfall grows with the rates: one point at 10 and 10, fifteen points at 50 and 30.

Order does not matter here, because multiplication commutes. 25 then 20 equals 20 then 25.

Order does matter once a coupon is involved

A flat amount and a percentage are not interchangeable, and the sequence is worth money.

A 200 item, a 50-off coupon, and a 20 percent promotion:

• Coupon first: 200 - 50 = 150, then 150 x 0.80 = 120.
• Percentage first: 200 x 0.80 = 160, then 160 - 50 = 110.

Ten units, on one item. The difference is exactly the percentage that would have been applied to the coupon's face value, so it scales with both the coupon and the rate.

Most tills default to coupon-first, which is the order that favours the shop. If the terms do not specify and the cashier has a choice, percentage-first is the one to ask for.

Tax order, and why the receipt tells you

Two conventions turn up in US retail:

• Discount, then tax. The usual one. Tax is computed on the reduced price.
• Tax on the pre-discount price. Occasionally seen with manufacturer coupons, where the retailer is reimbursed the coupon's value and the state wants tax on the full sale.

A 100 item, 20 percent off, 10 percent tax:

• Discount first: 100 x 0.80 = 80, then 80 x 1.10 = 88.
• Tax first: 100 x 1.10 = 110, then 110 - 20 = 90.

Two units on a small purchase, and it scales linearly with the price. The line-item order on the receipt tells you which one you got.

Markup and discount are not opposites

This is the section the original version of this article got wrong, so it is worth doing carefully.

Buy for 50, sell for 100, and that is a 100 percent markup. Put the same item on sale at 50 and that is a 50 percent discount. Same 50 units moving, two different percentages, because markup divides by cost and discount divides by the shelf price.

The consequence people get backwards: 100 percent markup followed by 50 percent off is exactly break-even. The shop receives 50, which is what it paid, before rent, wages and the card processing fee. It is not a profitable trick, it is a sale at cost.

The general relationship is clean. A markup of m returns the seller to cost at a discount of:

break-even discount = m / (1 + m)

So 50 percent markup breaks even at 33.3 percent off, 100 at 50, and 200 at 66.7. Anything deeper than that line is a genuine loss on the unit, which is why the deepest end-of-season reductions really are the shop giving up rather than a clever margin play.

The number retailers actually control

The arithmetic above is honest. The input marked "original price" is the part that is sometimes fiction.

A jacket "was 200, now 80" is a 60 percent discount only if anyone ever paid 200. If it sold at 120 everywhere for a year, the real discount is a third. The formula is not lying; it is being fed a number chosen for how it makes the second number look.

The antidote is a price history rather than a calculator. The Wayback Machine holds old product pages, and camelcamelcamel tracks Amazon prices over time.

One tool this article used to recommend is no longer a good idea: the Honey extension. Since December 2024 it has been the subject of consolidated class-action litigation in the Northern District of California over allegations that it replaced other parties' affiliate codes with its own. Separately, it is a browser extension with access to every shopping page you visit, which is exactly the category our privacy guide suggests keeping small.

Baskets: divide, do not average

For a cart with mixed discounts, the honest summary is money saved over money originally asked.

A 200 item at 50 percent off saves 100. A 20 item at 25 percent off saves 5.

105 / 220 = 47.7%

Averaging the two rates gives 37.5 percent, which treats the 20 item as equal in weight to the 200 one. Your wallet does not.

The case where percentages really do add

Two rates add when both are computed against the same original and applied separately, rather than one after the other.

A 10 percent state rebate and a 15 percent manufacturer rebate, both calculated on the sticker price and paid out as separate refunds, come to 25 percent of the original. That is genuinely additive.

The test is the baseline. Same baseline, they add. One applied to the output of the other, they multiply. Retail is nearly always the second; rebate and tax-credit programmes are often the first.

Tips are the same arithmetic, upward

total = subtotal x (1 + tip)

A 20 percent tip on 40 is 40 x 1.20 = 48. It is discount maths with the sign flipped, which is why the Tip Calculator and the discount calculator are the same machine underneath. The tip version adds bill splitting, which is where the arithmetic actually gets fiddly.

Three rules that cover almost everything

1. Stacked percentages multiply. Expect less than the sum, and much less when the rates are large.
2. Ask for the percentage before the flat coupon, and read the receipt for the tax order.
3. The "original price" is the number with the least accountability attached to it.

Get those three and the calculator is confirming what you already worked out.