Discount Calculator
The ticket, the markdowns and the coupon
Your result will appear here
Fill in the fields on the left and this updates as you type.
Know what this estimate is based on
- Jurisdiction
- General mathematical model
- Scope and limitations
- Planning indicator only. It does not assess every part of a household's finances or replace individualized professional advice.
- Source links checked
- Jul 30, 2026
Built and regression-tested by Smart Tools Lab. It has not been individually reviewed by a licensed financial, tax, or legal professional.
How to use
- 01
Enter the ticket price — the number on the tag before anything comes off. On its own it produces the markdown ladder below, which prices every common percentage off that one price at once.
- 02
Enter the percentage off on the tag. The page reports what the item costs after it and how much came off, which is the easy half of the arithmetic.
- 03
Enter any extra percentage that stacks at the register. This is where the page earns its keep: the second discount comes off the already-reduced price, so two markdowns never add up to their sum.
- 04
Enter a dollar-amount coupon or gift card. This is the only input whose POSITION in the chain changes what you pay, so the page computes both orders and prices the gap between them.
- 05
Enter your combined sales tax rate — zero in the five states with no statewide sales tax — and, in Advanced options, a total discount you are holding out for. The page then runs backwards to the exact price that hits it and the further percentage still needed.
Formula
Percentages multiply through what you KEEP. Keep fraction = (1 − first % ÷ 100) × (1 − second % ÷ 100), and the combined discount is 1 − that. Price after the tag markdown = ticket × (1 − first %). Price after the stacked markdown = that × (1 − second %). Coupon applied last (the cheaper order) = max(0, that − coupon). Coupon applied first = max(0, ticket − coupon) × keep fraction. The gap between the two orders = coupon × the combined discount fraction, exactly. True percentage off = (ticket − final price) ÷ ticket. You save the ticket minus the final price. Sales tax = final price × your rate; at the register you pay final price + tax. Working backwards, the price that hits a target discount = ticket × (1 − target %), and the further percentage still needed from where you are = 1 − (that target price ÷ your current price).
Example
A $129.00 ticket, 30% off on the tag and a further 15% at the register. The 30% takes $38.70 and leaves $90.30. The 15% is then taken on that $90.30, not on the ticket, so it comes to $13.55 rather than the $19.35 it would be worth against the original — a gap of $5.80. The final price is $76.76, which is 40.5% off, not the 45% the two numbers add up to, and you save $52.25. You are paying 59.5% of the ticket. Add a $20 coupon at the end and the price falls to $56.75, taking the true discount to 56.0%; hand that same coupon over BEFORE the percentages and you pay $64.86 instead — $8.10 worse, which is exactly $20 × 40.5%. At an 8% combined sales tax rate the tax on the $56.75 is $4.54 and the register total is $61.30, against the $10.32 of tax the undiscounted ticket would have carried.
Definitions
- Keep fraction
- What is left after a discount — 1 minus the rate. Chains of percentage discounts are multiplied through their keep fractions, which is why they never add.
- Stacked discount
- A second markdown applied at the register on top of the price on the tag. It is taken on the already-reduced price, so it is worth less in dollars than its own percentage against the ticket.
- True percentage off
- The whole chain measured against the original ticket: (ticket − what you pay) ÷ ticket. Always less than the sum of the percentages involved.
- Order of operations
- Where a dollar coupon sits in the chain. Percentages commute with each other; a dollar amount does not commute with them, and the difference is the coupon times the combined discount.
- Anchor or 'compare at' price
- A former or reference price a discount is quoted against. FTC guidance at 16 C.F.R. Part 233 requires it to have been a genuine, actively offered price rather than one set to make the markdown look larger.
Good to know
Why stacked discounts do not add
Two markdowns never total their sum, and the reason is one line long: the second one is taken on the already-reduced price rather than on the ticket. Twenty per cent off leaves you paying 80%; a further 10% off leaves 90% of that; 0.80 × 0.90 = 0.72, so you pay 72% of the ticket and the true discount is 28% rather than 30%. The general rule is to multiply what you KEEP rather than adding what comes off, and it extends to any number of discounts. The shortfall is not arbitrary either — it is exactly the two percentages multiplied together, read as points. Twenty and ten give 2 points of shortfall, which is the gap between 30% and 28%. Thirty and fifteen give 4.5 points: 45% claimed, 40.5% real, and on a $129 ticket that is $76.76 rather than the $70.95 a naive sum predicts. Fifty and twenty give 10 points, so 70% claimed is 60% real. Forty and forty give 16 points, so two enormous-sounding markdowns come to 64% off rather than 80%. Notice which direction this always runs: the error favours the store, it grows as the discounts grow, and it is largest on precisely the deals that are advertised most loudly. The single exception is a dollar coupon, which genuinely does subtract — and which is why it gets its own box.
Off, of, and the arithmetic that never goes wrong
The most expensive small error in retail is reading 'off' as 'of'. Forty per cent OFF means you pay sixty per cent OF the ticket, and confusing the two is a forty-point mistake in whichever direction you make it. There is one habit that removes the problem permanently: subtract the percentage from 100 first, then multiply. A 30% sign becomes 'pay 70%', a 15% sign becomes 'pay 85%', and a chain becomes a product you can do in your head — 70% of 85% is a shade under 60%, so you are paying about 60 cents on the dollar and saving about 40. Doing it that way also makes stacking self-evident, because 80% of 90% is plainly 72% and nobody, having written that down, would call it thirty per cent off. For rougher work in an aisle, the useful anchors are the ones that halve or tenth cleanly: 50% off is half; 25% off is half of a half taken away; 10% is the decimal moved one place; 30% is three of those; 33% is a third off, so multiply by two-thirds. And one sanity check that catches most errors before they cost anything: the price after any single discount must lie between zero and the ticket, and after two it must lie below the first one's result.
The dollar coupon is the only thing whose order matters
Percentages commute with each other. Thirty then fifteen and fifteen then thirty both land on 59.5% of the ticket, so a register applying them in either sequence charges the same. A dollar amount does not commute with a percentage, and the difference is real money. Apply a $20 coupon AFTER a 40.5% combined markdown and it is worth its full $20: the $76.76 becomes $56.75. Apply it first and the percentages then come off a number the coupon has already shrunk, so $129 less $20 is $109, and 59.5% of $109 is $64.86 — $8.10 worse. That gap is not a rounding artefact; it is exactly the coupon multiplied by the combined discount fraction, $20 × 40.5%, and it grows with both. Registers genuinely differ on the sequence, store policy differs by promotion, and the receipt is the only authority on which one you got — the itemised lines show the order the system used. It is the one thing on a sale price worth raising at a till, because the fix is a re-ring rather than an argument. The same asymmetry is why a gift card is not a coupon: a gift card is a method of payment applied at the very end, so it is always worth its face value.
The anchor the percentage is taken from, and the tax on the end
A discount is a percentage of something, and it is only as honest as that something. A 'compare at' or 'was' price the item never actually sold at makes the whole calculation arithmetic without meaning, and it is a legal question as well as a rhetorical one: the FTC's Guides Against Deceptive Pricing at 16 C.F.R. Part 233 turn on whether the former price was one at which the article was openly and actively offered for a reasonably substantial period, in good faith, and not for the purpose of establishing a fictitious higher price. Outlet-only merchandise made to a price point, permanent 'sales' that never end, and manufacturer list prices nobody has ever charged all sit in that territory. The shopper's test is simpler than the legal one and works every time: would this thing have been worth the final price to you if the tag had simply said the final price, with no percentage anywhere near it? Then the tax. Sales tax lands on what you actually pay after a store's own markdown, never on the ticket, so a discount quietly saves you the tax on the part that came off as well — on a $129 ticket cut to $56.75 at 8%, that is $5.78 of tax saved on top of $72.25 of price. Rates are state and local law and the spread is wide: five states levy no statewide sales tax, California's 7.25% is the highest statewide rate, and combined state-and-local rates pass 10% in parts of several states.
Frequently asked questions
Is 20% off then 10% off the same as 30% off?
No — it is 28% off. The second discount is applied to the already-reduced price rather than to the ticket, so it is worth less than its own number suggests: on $100, the first 20% takes $20 and the second 10% takes $8 rather than $10. The shortfall is always the two percentages multiplied together, expressed in points: 20 × 10 ÷ 100 = 2 points, which is precisely the gap between 30% and 28%. The only discounts that genuinely add are dollar amounts.
How do I work out the true percentage off a stacked sale?
Multiply what you KEEP, not what comes off. A 30% discount leaves 70%, a further 15% leaves 85% of that, so you keep 0.70 × 0.85 = 0.595 — you pay 59.5% of the ticket and the true discount is 40.5%, not the 45% the two numbers add to. On a $129 ticket that is $76.76 rather than the $70.95 a naive sum would predict, a difference of $5.80. The rule generalises to any number of percentage discounts: multiply the keep-fractions.
Does the coupon come off before or after the percentage discounts?
It matters, and it is the one thing on this page worth querying at a register. Applied AFTER the percentages, a $20 coupon is worth its full $20. Applied first, the percentages then come off a number the coupon has already shrunk, so it is worth only $20 × (1 − the combined discount). On a $129 ticket at 30% then 15%, coupon-last leaves $56.75 and coupon-first leaves $64.86 — $8.10 worse, which is exactly $20 × 40.5%. Registers differ, and the receipt shows the order the one in front of you used.
Is sales tax charged on the ticket price or on the sale price?
On what you actually pay after the store's own markdown, which means a discount quietly saves you the tax on the part that came off as well. On a $129 ticket discounted to $56.75 at an 8% rate, the tax is $4.54 rather than the $10.32 the ticket would have carried — $5.78 of tax saved on top of the $72.25 of price. A manufacturer's coupon is treated differently in some states, because the store is reimbursed for it, so the receipt is the authority on your own.
What is the difference between 40% off and 40% of?
Forty points, and the two get swapped constantly. Forty per cent OFF means you pay sixty per cent OF the ticket. Read every sale sign the same way: subtract the percentage from 100 first, then multiply. Doing it that way also makes stacking obvious, because 80% of 90% is plainly 72% and nobody would look at 72% and call it thirty per cent off.
How do I work backwards from the discount I am waiting for?
Put the total discount you are holding out for into Advanced options. The page names the exact price that hits it — a 60% target on a $129 ticket is $51.60 — and, from wherever your chain currently leaves you, the further percentage still needed to get there. That last figure is usually much smaller than the gap in the headline percentages suggests, which is the whole of the buy-now-or-wait decision.
How do I know the 'was' price was ever real?
You often cannot, and it is a legal question rather than only a rhetorical one. The FTC's Guides Against Deceptive Pricing at 16 C.F.R. Part 233 turn on whether the former price was one at which the article was openly and actively offered for a reasonably substantial period, in good faith and not for the purpose of establishing a fictitious higher price. A 'compare at' number an item never sold at makes any percentage taken from it arithmetic without meaning. The shopper's test is simpler: would this have been worth the final price to you if the tag had simply said the final price?
Do cash-back cards and store discounts stack the same way?
They stack multiplicatively, exactly like two markdowns. A 2% card on top of a 40.5% chain leaves you paying 59.5% × 98% = 58.31% of the ticket, so the true total is 41.69% off rather than 42.5%. The 2% is applied to what you actually charge, which is the discounted price — so like every percentage in the chain, it is worth less than its own number against the original ticket.