See the final price after a percentage discount and exactly how much money you save.
How the Discount Calculator works
The discount calculator turns a percent-off (or stacked percents) into the exact sale price and the dollars you save, using Sale price = Original x (1 - discount%). It is built for retail savings, not seller pricing, so every output is framed as what you pay and what you keep.
The variables are: Original = the list or sticker price in dollars; discount% = the markdown as a decimal (25% = 0.25); Sale price = what you actually pay; and You save = Original x discount% (the gap between the two). The core identities are Sale price = Original x (1 - discount%) and You save = Original - Sale price.
Here is exactly what the tool does internally:
- Reads the original price and converts each discount from a percent to a decimal by dividing by 100.
- For a single discount, multiplies Original x (1 - discount%) to get the sale price.
- For stacked discounts, applies each one in sequence to the running price - never adding them - because the second percent comes off an already-reduced number.
- Computes You save as Original minus the final sale price, plus the effective single discount that the stack equals.
- Optionally applies sales tax to the discounted price so you see the out-the-door total.
- Can run in reverse: given a sale price and a discount, it solves Original = Sale price / (1 - discount%).
Edge cases it handles: a 0% discount returns the original unchanged; a 100% discount returns $0 (free); stacked percents are multiplied, so 20% then 10% yields 28% off, not 30%; and it keeps percent-off separate from dollar-off, since a flat $15 coupon is not a percentage. To work the seller side instead, use the markup calculator; for pure percentages with no retail framing, use the percentage calculator.
Example calculation
Here are three distinct retail scenarios, each figure recomputed with Sale = Original x (1 - discount%).
Example 1 - a single percent-off with tax. A jacket lists at $120.00 at 25% off, in a state with 6.5% sales tax. Sale price = 120 x (1 - 0.25) = $90.00, so you save 120 x 0.25 = $30.00. Tax is charged on the discounted price: 90 x 0.065 = $5.85, for an out-the-door total of $95.85. Tax never applies to the $30 you saved.
Example 2 - stacked discounts (the trap). A coat lists at $250.00 with 40% off plus an extra 15% off coupon. Applied in sequence: 250 x (1 - 0.40) = $150.00, then 150 x (1 - 0.15) = $127.50. You save $122.50, an effective 49% off, not the 55% you would get by adding 40 + 15. The naive "55% off" math would wrongly predict $112.50 - a $15.00 mistake in the store's favor.
Example 3 - working backward. A tag reads $63.75 and says 25% off. The original was Sale / (1 - discount%) = 63.75 / 0.75 = $85.00, confirming a true $21.25 markdown. This is how you verify a "was/now" claim is real.
| Scenario | Original | Discount(s) | Sale price | You save | Effective % |
|---|---|---|---|---|---|
| Jacket (pre-tax) | $120.00 | 25% | $90.00 | $30.00 | 25% |
| Coat (stacked) | $250.00 | 40% + 15% | $127.50 | $122.50 | 49% |
| Backward solve | $85.00 | 25% | $63.75 | $21.25 | 25% |
The takeaway from Example 2 is the one shoppers miss most: stacked percents multiply, they do not add. Two discounts of 40% and 15% land at 49% off because the 15% only ever comes off the $150.00 that is left, not the full $250.00.
Tips for using the Discount Calculator
- Stacked discounts multiply, they never add. To get the real combined rate, compute 1 - (1 - first) x (1 - second). For 20% then 10%, that is 1 - 0.90 x 0.80 = 0.28, so 28% off, not 30%.
- Order does not matter for two percentages - 40% then 15% equals 15% then 40% - because multiplication commutes. The store applying the bigger discount first changes nothing about your final price.
- Order DOES matter when you mix a percent and a flat dollar coupon. On an $80.00 item, taking $10 off then 25% off leaves $52.50, but 25% off then $10 off leaves $50.00. Ask the cashier to apply the percent first.
- Sales tax does not change with discount order either: a 30% markdown then 7% tax equals 7% tax then 30% off. What matters is that tax is charged on the lower, discounted price, so a store coupon also shrinks your tax.
- To verify a 'was/now' price, divide the sale price by (1 - discount%). If $63.75 is marked 25% off, the original should be 63.75 / 0.75 = $85.00; if the tag claims a higher 'was' price, the discount is inflated.
- Convert BOGO deals to a real percentage before comparing. Buy-one-get-one-free is 50% off, buy-2-get-1-free is 33.3% off, and buy-3-get-1-free is only 25% off - but only if you actually need every unit.
- A 'BOGO 50% off' (second item half price) is just 25% off the pair, because you pay 1.5 items' worth for 2. It is far weaker than true BOGO-free, despite sounding similar.
- Compare a percent-off coupon against a flat dollar coupon at the break-even price = dollar amount / discount rate. A $15 coupon beats 20% off below $75.00, and 20% off wins above $75.00.
- An 'extra 50% off clearance' stacked on an original 30%-off tag is 65% off total (0.70 x 0.50 = 0.35 of the price remains), not 80% off. Always multiply the remaining fractions.
- Tax-free holidays remove the tax leg entirely, so on a $90.00 post-discount item at 6.5% tax you keep the $5.85 - effectively another small discount on top of the markdown.
Stacked discounts vs adding the percentages: why 20% + 10% is 28%, not 30%
Stacked discounts are applied one after another to a shrinking price, so they multiply rather than add - 20% then 10% comes out to 28% off, not 30%. This is the single most common shopper mistake, and stores rely on it because the stacked number always sounds bigger than it is.
The rule is: combined remaining fraction = (1 - first) x (1 - second), and effective discount = 1 minus that. For 20% and 10%, 0.80 x 0.90 = 0.72, so 28% comes off. The table below shows common pairs, every figure recomputed on a $100.00 item.
| Discounts stacked | If you wrongly add | True sale price ($100) | True effective discount |
|---|---|---|---|
| 20% then 10% | 30% | $72.00 | 28% |
| 30% then 20% | 50% | $56.00 | 44% |
| 40% then 15% | 55% | $51.00 | 49% |
| 50% then 20% | 70% | $40.00 | 60% |
| 30% then 20% then 10% | 60% | $50.40 | 49.6% |
The gap between the added number and the real one grows as the discounts get bigger: a 20%/10% stack is off by 2 points, but a 50%/20% stack is off by a full 10. To check any single percentage by itself, the percentage calculator handles plain percent-of math; this tool is the one that chains them correctly.
Common discount mistakes to avoid
Most discount errors come from adding stacked percents, mishandling coupon order, or trusting an inflated 'original' price. Avoid these six:
- Adding stacked discounts: 25% plus an extra 20% is not 45% off; it is 1 - 0.75 x 0.80 = 40% off. Always multiply the remaining fractions.
- Assuming BOGO equals 50% off when you do not need both items: if you only wanted one, buying two to get the deal is a 0% saving on what you actually needed.
- Letting the cashier apply a dollar coupon before a percent coupon: on mixed coupons, percent-first saves you more. Order is irrelevant only when both are percentages.
- Believing an inflated 'was' price: verify with Original = Sale / (1 - discount%); if the math does not match the tag, the markdown is fake.
- Forgetting tax is on the discounted price: your store coupon shrinks the tax too, so do not compute tax on the full sticker.
- Confusing a percent-off with a dollar-off: a flat $20 coupon is a different animal from 20% off and only matches at one specific price ($100.00, in that case).
How to calculate a discount by hand or in Excel
By hand, multiply the price by (1 - the discount as a decimal); in Excel the sale price is =Price*(1-Discount). No special function exists because a discount is just multiplication.
For a $120.00 item at 25% off, with the price in A2 and the rate (as 0.25, or a cell formatted as 25%) in B2:
- Sale price: =A2*(1-B2) returns 90.
- You save: =A2*B2 returns 30.
- Sale price plus 6.5% tax: =A2*(1-B2)*1.065 returns 95.85.
For stacked discounts with the second rate in C2, chain the factors: =A2*(1-B2)*(1-C2). To find the effective single discount of the stack, use =1-(1-B2)*(1-C2). To work backward from a sale price in D2 to the original, divide: =D2/(1-B2). Keep every rate as a decimal (or percent-formatted cell) and never use =FV() or =PMT() here - those assume interest and time, which a one-shot discount has neither of. For the seller-side version of this math, see the markup calculator, which goes the other direction from cost to price.
Percent-off vs dollar-off: which coupon saves more?
A flat dollar-off coupon beats a percent-off coupon on cheap items, and a percent-off wins on expensive items, with the crossover at break-even price = dollar amount / discount rate. The two are only equal at that one price.
Compare a $15-off coupon against a 20%-off coupon. They tie at 15 / 0.20 = $75.00. Below $75.00 the flat $15 saves more; above $75.00 the 20% pulls ahead. Every figure below is recomputed:
| Item price | $15 flat off (you pay) | 20% off (you pay) | Better choice |
|---|---|---|---|
| $50.00 | $35.00 | $40.00 | $15 flat |
| $75.00 | $60.00 | $60.00 | Tie |
| $100.00 | $85.00 | $80.00 | 20% off |
| $200.00 | $185.00 | $160.00 | 20% off |
The practical rule: use the flat coupon on small baskets and the percentage on big ones. When you have both and the store allows stacking, apply the percent first, since taking the fixed dollar amount off after the percentage leaves a larger base for the percentage to work on. To sanity-check the raw percentage on any single price, the percentage calculator handles it.
Turning BOGO and 'buy 2 get 1' into real percentages
Multi-buy deals only become comparable once you convert them to an effective percent off, calculated as 1 - (items paid / items received). The headline almost always overstates the value.
| Deal | You pay for | You get | Effective discount |
|---|---|---|---|
| Buy one get one free | 1 | 2 | 50% off |
| BOGO 50% off (second half price) | 1.5 | 2 | 25% off |
| Buy 2 get 1 free | 2 | 3 | 33.3% off |
| Buy 3 get 1 free | 3 | 4 | 25% off |
The catch is the denominator: these percentages only hold if you genuinely need every unit. A buy-2-get-1-free deal on something you would have bought one of is not 33% off - it is paying double for a spare you did not want. A true BOGO-free at 50% off is strong; the look-alike 'BOGO 50%' (second item half price) is only 25% off the pair. Once you have the effective rate, drop it into this discount calculator like any other percent-off to compare it head-to-head against a straight markdown.
Does discount before or after sales tax matter?
For a single discount and a single tax, the order does not change your total - a 30% markdown then 7% tax equals 7% tax then 30% off - because both are just multiplications. What actually matters is that US sales tax is charged on the discounted price, so a store coupon shrinks your tax bill too.
Take a $200.00 item at 30% off with 7% tax. Discount-then-tax: 200 x 0.70 x 1.07 = $149.80. Tax-then-discount: 200 x 1.07 x 0.70 = $149.80. Identical. The reason cashiers always ring the discount first is simply that tax is legally assessed on the reduced amount you pay, not on the sticker.
Two real wrinkles do change the math: manufacturer coupons in some states are taxed on the pre-coupon price (because the store is reimbursed by the brand), while store coupons reduce the taxable amount; and a tax-free holiday removes the tax leg entirely, effectively adding a small extra discount. To handle the tax leg precisely on its own, use the sales tax calculator.
Is the discount actually good? Retail benchmarks
In US retail, a 'sale' under about 15% off is barely meaningful, 25-40% is a solid everyday markdown, and 50%+ usually signals clearance or end-of-season - but the real test is the effective price, not the percent. Use these reference points to judge a deal:
| Discount depth | Typical meaning | Shopper read |
|---|---|---|
| 5% - 10% | Token coupon, loyalty perk | Nice, rarely worth waiting for |
| 15% - 25% | Standard promo / seasonal sale | Decent; common several times a year |
| 30% - 40% | Real markdown event | Good; a genuine buy signal |
| 50% - 70% | Clearance / end of season | Strong, but check stock and returns |
| 75%+ | Final clearance, discontinued | Best price, often non-returnable |
These are general patterns, not any one retailer's policy. The deeper trap is anchoring: a 60%-off tag means nothing if the 'original' was inflated, so verify the real markdown with Original = Sale / (1 - discount%). And remember that even a great percent off is only a saving on something you needed - a 70%-off impulse buy still costs 30% of money you would otherwise have kept. To check a single percentage figure outside the retail frame, the percentage change calculator shows the raw before-to-after move.
Stacked discounts and BOGO quick-reference (true percent off)
Stacked percentages never add up to their sum - the second cut only applies to the already-reduced price, so multiply the remaining fractions instead. The table below shows the real effective discount and what a $100.00 item costs for the most common shopper combinations. Every figure is recomputed; for example 30% then 20% off gives 0.70 x 0.80 = 0.56, meaning you pay 56% and save 44%.
| Advertised deal | What shoppers assume | True % off | Cost of a $100 item |
|---|---|---|---|
| 20% off, then 10% off | 30% off | 28% off | $72.00 |
| 25% off, then 15% off | 40% off | 36.25% off | $63.75 |
| 30% off, then 20% off | 50% off | 44% off | $56.00 |
| 30% off, then extra 40% off | 70% off | 58% off | $42.00 |
| 50% off, then extra 25% off | 75% off | 62.5% off | $37.50 |
| Three 20%-off coupons | 60% off | 48.8% off | $51.20 |
| Buy 2 get 1 free (equal price) | 33% off | 33.3% off | $66.67 |
| Buy 3 get 1 free (equal price) | 25% off | 25% off | $75.00 |
Read the table as fractions that remain, not percentages that add: the 'three 20%-off coupons' row is 0.80 x 0.80 x 0.80 = 0.512, so you pay 51.2% and save 48.8% - never the 60% the headline implies. For the multi-buy rows, the percent only holds if you actually use every unit you are forced to buy.
Related on this site
Percentage Calculator · Sales Tax Calculator · Markup Calculator · Percentage Change Calculator · Unit Price Calculator · Tip Calculator
For a related deep dive, see FTC: how to spot fake discounts.
Discount Calculator — frequently asked questions
- Stacked discounts?
- Apply them sequentially — 20% then 10% is not 30% off, it is 28% off.
- Discount before or after tax?
- Discounts are normally applied before sales tax is added.
- How do stacked discounts work?
- 20% then 10% off equals 28% off, not 30% — they apply one after another.
- Is the discount before or after tax?
- Discounts normally apply before sales tax is added.
- Is 30% off then 20% off the same as 50% off?
- No - 30% off then 20% off equals 44% off, not 50%, because the second discount applies to the already-reduced price. On a $250.00 item: $250 x 0.70 = $175.00, then $175 x 0.80 = $140.00. You save $110.00, which is 44% of $250.00. Stacked percentages always come out lower than their sum. To check any pair, multiply the remaining fractions (0.70 x 0.80 = 0.56, so 44% off).
- What does "extra 40% off" already-reduced clearance actually save me?
- An extra 40% off an item already marked 30% off is 58% off the original, not 70%. On a $90.00 clearance tag: $90 x 0.70 = $63.00, then $63 x 0.60 = $37.80. You save $52.20. The mistake is adding 30 + 40 = 70%. Instead multiply: 0.70 x 0.60 = 0.42, meaning you pay 42% and save 58%. The <a href="/discount-calculator/">discount calculator</a> stacks them for you.
- How do I find the original price from a sale price?
- Divide the sale price by (1 minus the discount as a decimal). If something is 30% off and rings up at $63.00, the original was $63 / 0.70 = $90.00. For a $45.00 item at 25% off: $45 / 0.75 = $60.00. For an $89.99 price at 40% off: $89.99 / 0.60 = $149.98. Never multiply the sale price by the discount to get the original - that undershoots the real list price.
- What percent off is buy-one-get-one-free?
- BOGO free is exactly 50% off when both items cost the same. Buy two $40.00 shirts and pay $40.00 for the pair: $40 paid out of $80.00 retail is 50% off, or $20.00 off each. If the free item is the cheaper one, the discount is less than 50%, because your savings equal only the lower-priced item divided by the combined total. Use the <a href="/discount-calculator/">discount calculator</a> on the per-item price to confirm.
- What is the effective discount on "buy 2 get 1 free"?
- Buy 2 get 1 free is 33.3% off when all three items are the same price - you pay for 2 and take home 3, so 2 paid out of 3 received. At $30.00 each you pay $60.00 for $90.00 of goods, saving $30.00 (33.3%). By the same paid-over-received rule, buy 3 get 1 free is 25% off (pay 3 of 4), and buy 4 get 2 free is also 33.3% off (pay 4 of 6).
- Does a discount get applied before or after sales tax?
- Stores apply the discount first, then charge sales tax on the lower, discounted price - so you are taxed on less. A $200.00 item at 25% off is $150.00, and 8% tax on $150.00 is $12.00, for a $162.00 total. Without the discount, 8% tax on $200.00 would be $16.00. You save $50.00 on the item plus $4.00 in tax, $54.00 total. Tax is never calculated on the original price after a markdown.
- Is $20 off better than 20% off?
- It depends entirely on the price - a flat $20 off beats 20% off only when the item costs under $100.00. On a $50.00 item, $20 off is 40% off (far better than 20% off, which is just $10.00). On a $200.00 item, $20 off is only 10% off, while 20% off saves $40.00. The break-even is exactly $100.00, where both equal $20.00. Compute the dollar amount each way and take the larger.
- Does the order of a percent coupon and a dollar coupon matter?
- Yes - applying the percent off first usually saves you more than applying the dollar coupon first. On a $100.00 item with 15% off plus a $10 coupon: 15% first gives $100 x 0.85 = $85.00, then -$10 = $75.00. The $10 first gives $90.00, then x 0.85 = $76.50. The percent-first order saves an extra $1.50 here. Always run the percentage discount before subtracting a fixed-dollar coupon when the register lets you.
- What percent off am I getting if it dropped from $129.99 to $99.99?
- That is about 23% off - divide the savings by the original price. The savings are $129.99 - $99.99 = $30.00, and $30 / $129.99 = 0.2308, or 23.08% off. For $75.00 down to $60.00: $15 / $75 = 20% off. Always use savings divided by the original, not savings divided by the sale price (that overstates the deal). The <a href="/percentage-change-calculator/">percentage-change calculator</a> handles this too.
- How do I calculate a discount in Excel?
- Use =price*(1-percent) for the sale price and =price-sale for the savings, entering the percent as a decimal or with a % sign. For $120.00 at 25% off: =120*(1-0.25) returns 90, and =120-90 returns 30. For stacked discounts, chain the factors: =250*(1-0.30)*(1-0.20) returns 140. To find the original from a sale price, use =sale/(1-percent), so =63/(1-0.30) returns 90.
- Is 50% off plus an extra 25% off the same as 75% off?
- No - 50% off then an extra 25% off is 62.5% off, not 75%. On a $100.00 item: $100 x 0.50 = $50.00, then $50 x 0.75 = $37.50, so you save $62.50. Adding the two percentages (50 + 25 = 75) overstates the deal by $12.50. The shortcut is to multiply what remains: 0.50 x 0.75 = 0.375, meaning you pay 37.5% and save 62.5%.
- What original price do I need so the sale price is the amount I want to pay?
- Divide your target spend by (1 minus the discount). To pay exactly $100.00 on a 20%-off item, the original must be $100 / 0.80 = $125.00. To pay $50.00 at 30% off, look for items originally $50 / 0.70 = $71.43 or less. This is the reverse of a normal discount and is handy for budgeting a sale trip: set your spend, then shop the rack at or below that ceiling price.
- Is stacking three 20% off coupons the same as 60% off?
- No - three 20%-off discounts stacked equal 48.8% off, not 60%. On a $100.00 item: $100 x 0.80 x 0.80 x 0.80 = $51.20, so you save $48.80. Each coupon only cuts the already-reduced balance. Four 10%-off coupons land at 34.4% off ($100.00 falls to $65.61), not 40%. The rule: multiply the remaining fractions together; stacking can never reach the simple sum of the percentages.
- How much do I save with 25% off then 15% off on an $80 item?
- You save $29.00 - the price falls to $51.00, which is 36.25% off, not 40%. Step by step: $80 x 0.75 = $60.00, then $60 x 0.85 = $51.00. The savings are $80 - $51 = $29.00. Adding 25 + 15 = 40% would wrongly suggest a $48.00 price ($32.00 saved). Multiply the remaining fractions (0.75 x 0.85 = 0.6375) to get the true 63.75% paid and 36.25% saved.
- Is a discount calculator different from a markup or percentage calculator?
- Yes - a discount calculator works from the buyer's side (price minus a percent off equals what you pay), while a <a href="/markup-calculator/">markup calculator</a> works from the seller's side (cost plus a percent equals selling price). They are not reverses of each other: a 25% markup is undone by a 20% discount, not a 25% one (1 / 1.25 = 0.80). A plain <a href="/percentage-calculator/">percentage calculator</a> finds any percent of a number but does not chain stacked sales or back out the original price.
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