To calculate a discount, multiply the price by (1 − percent ÷ 100). 40% off $60 is $60 × 0.60 = $36, saving $24. 30% off $40 is $28, and 20% off $100 is $80. Two discounts in a row multiply, so 20% off then 10% off is 28% off, not 30%.
This discount calculator gives the sale price and your savings, stacks an extra discount, adds sales tax, and works backwards from a sale price to the original price. All you need is the tag price and the discount.
How to use this calculator
- Enter the original price and the percent off.
- For an "extra 10% off sale prices" deal, put the second discount in "Extra % off".
- Add your sales tax rate to see what you pay at the register.
- Switch to "Original price from sale price" to find what an item cost before the discount.
Discount formula: how to calculate a discount
OpenStax Prealgebra states the discount rule in two lines: amount of discount = discount rate × original price, and sale price = original price − discount. Combining them gives the one-step version used by this calculator, sale price = price × (1 − rate). Every formula below is a rearrangement of the same idea.
- Sale price = price × (1 − % ÷ 100)
- You save = price × % ÷ 100
- Stacked discounts = price × (1 − a ÷ 100) × (1 − b ÷ 100)
- Original price = sale price ÷ (1 − % ÷ 100)
- With tax = sale price × (1 + tax rate ÷ 100)
A quick mental shortcut: 10% off moves the decimal one place (10% of $38 is $3.80), so 20% is double that and 30% is triple. 50% off is half, and 25% off is a quarter less.
Discount computation, step by step
Here is the full computation for 40% off a $25 item, the kind of line a register or invoice works through:
- Write the rate as a decimal: 40% = 40 ÷ 100 = 0.40.
- Find the amount of discount: 0.40 × $25 = $10.
- Subtract from the original price: $25 − $10 = $15.
- Check with the shortcut: you pay 60% of the price, and 0.60 × $25 = $15.
- If sales tax applies, multiply the sale price by (1 + tax rate). At 7% tax, $15 × 1.07 = $16.05.
OpenStax's worked example follows the same steps: a $140 dress discounted 35% has a discount of 0.35 × $140 = $49 and a sale price of $91. For an odd price such as $79.99 at 15% off, the discount is $12 and the price is $67.99; registers round the discount to the cent, so receipts can differ by a cent from a calculation kept to more decimals.
If you only need the percentage part of the question (for example "what is 40% of 25?"), the percentage calculator gives it directly, and the percentage increase calculator works out the percent change between a regular and a sale price in either direction.
Percent off chart
Sale prices for common prices from $10 to $500 at 10% to 75% off, before tax and rounded to the cent. Find your price in the left column and the discount along the top; for other prices, use the calculator.
| Price | 10% off | 15% off | 20% off | 25% off | 30% off | 35% off | 40% off | 50% off | 60% off | 70% off | 75% off |
|---|---|---|---|---|---|---|---|---|---|---|---|
| $10 | $9 | $8.50 | $8 | $7.50 | $7 | $6.50 | $6 | $5 | $4 | $3 | $2.50 |
| $15 | $13.50 | $12.75 | $12 | $11.25 | $10.50 | $9.75 | $9 | $7.50 | $6 | $4.50 | $3.75 |
| $20 | $18 | $17 | $16 | $15 | $14 | $13 | $12 | $10 | $8 | $6 | $5 |
| $25 | $22.50 | $21.25 | $20 | $18.75 | $17.50 | $16.25 | $15 | $12.50 | $10 | $7.50 | $6.25 |
| $30 | $27 | $25.50 | $24 | $22.50 | $21 | $19.50 | $18 | $15 | $12 | $9 | $7.50 |
| $35 | $31.50 | $29.75 | $28 | $26.25 | $24.50 | $22.75 | $21 | $17.50 | $14 | $10.50 | $8.75 |
| $40 | $36 | $34 | $32 | $30 | $28 | $26 | $24 | $20 | $16 | $12 | $10 |
| $45 | $40.50 | $38.25 | $36 | $33.75 | $31.50 | $29.25 | $27 | $22.50 | $18 | $13.50 | $11.25 |
| $50 | $45 | $42.50 | $40 | $37.50 | $35 | $32.50 | $30 | $25 | $20 | $15 | $12.50 |
| $60 | $54 | $51 | $48 | $45 | $42 | $39 | $36 | $30 | $24 | $18 | $15 |
| $70 | $63 | $59.50 | $56 | $52.50 | $49 | $45.50 | $42 | $35 | $28 | $21 | $17.50 |
| $75 | $67.50 | $63.75 | $60 | $56.25 | $52.50 | $48.75 | $45 | $37.50 | $30 | $22.50 | $18.75 |
| $80 | $72 | $68 | $64 | $60 | $56 | $52 | $48 | $40 | $32 | $24 | $20 |
| $90 | $81 | $76.50 | $72 | $67.50 | $63 | $58.50 | $54 | $45 | $36 | $27 | $22.50 |
| $100 | $90 | $85 | $80 | $75 | $70 | $65 | $60 | $50 | $40 | $30 | $25 |
| $120 | $108 | $102 | $96 | $90 | $84 | $78 | $72 | $60 | $48 | $36 | $30 |
| $125 | $112.50 | $106.25 | $100 | $93.75 | $87.50 | $81.25 | $75 | $62.50 | $50 | $37.50 | $31.25 |
| $150 | $135 | $127.50 | $120 | $112.50 | $105 | $97.50 | $90 | $75 | $60 | $45 | $37.50 |
| $175 | $157.50 | $148.75 | $140 | $131.25 | $122.50 | $113.75 | $105 | $87.50 | $70 | $52.50 | $43.75 |
| $200 | $180 | $170 | $160 | $150 | $140 | $130 | $120 | $100 | $80 | $60 | $50 |
| $250 | $225 | $212.50 | $200 | $187.50 | $175 | $162.50 | $150 | $125 | $100 | $75 | $62.50 |
| $300 | $270 | $255 | $240 | $225 | $210 | $195 | $180 | $150 | $120 | $90 | $75 |
| $400 | $360 | $340 | $320 | $300 | $280 | $260 | $240 | $200 | $160 | $120 | $100 |
| $500 | $450 | $425 | $400 | $375 | $350 | $325 | $300 | $250 | $200 | $150 | $125 |
How to find the percent off from two prices
When a tag shows only a "was" and "now" price, choose "Percent off from two prices" in the calculator, or work it out in three steps:
- Divide the sale price by the original price. $56 ÷ $80 = 0.70.
- Subtract that from 1. 1 − 0.70 = 0.30.
- Multiply by 100. The item is 30% off.
Odd prices work the same way: $129.99 cut to $99.99 is 23.08% off, so a sign saying "save 25%" on that item would be rounding up. Always divide by the original price. Dividing the $30 saving by the $99.99 sale price gives 30%, which overstates the deal.
Percent off plus a dollar-off coupon
A percentage and a fixed-dollar coupon don't combine the way two percentages do, because the order changes the answer. Take an $80 jacket at 25% off with a $10 coupon:
- Percent first, then coupon: $80 × 0.75 = $60, minus $10 = $50, which is 37.5% off overall.
- Coupon first, then percent: ($80 − $10) × 0.75 = $52.50, which is 34.4% off.
Taking the coupon last saves you more, and the gap grows with the discount rate. The calculator's "Dollar coupon" field applies the coupon after the percentages and reports the true total percent off. The coupon's terms decide the order at the register, so read them if the difference matters.
BOGO and multi-buy deals as a percent off
Multi-buy offers are easier to compare once they're turned into a percent off. When every item costs the same, the discount is 1 − (items you pay for ÷ items you get):
| Deal | You pay for | You get | Percent off each |
|---|---|---|---|
| Buy 1, get 1 free | 1 | 2 | 50% |
| Buy 1, get 1 50% off | 1.5 | 2 | 25% |
| Buy 1, get 1 25% off | 1.75 | 2 | 12.5% |
| Buy 2, get 1 free | 2 | 3 | 33.3% |
| Buy 3, get 1 free | 3 | 4 | 25% |
| Buy 3, get 2 free | 3 | 5 | 40% |
These are only worth it if you'd buy the extra items anyway. If the free item is the cheaper one, your real discount is smaller: a $30 shirt with a free $20 shirt is 40% off the pair, not 50%. The FTC's guide on the word "free" (16 CFR § 251.1) says that in a "Buy 1-Get 1 Free" offer you should pay no more than the regular price for the item you buy. It defines the regular price as the price the seller actively charged over a recent 30-day period. For prices that fluctuate, that means the lowest price at which substantial sales were made in that period. A store that marks up the first item to fund the free one isn't giving you 50% off.
Quick answers: X percent off Y
Searches like "20 40 percent off" or "60 30 percent off" can mean either order, so both are shown. The dollar savings match because x% of y equals y% of x, but the price you pay doesn't.
| Question | Sale price | You save |
|---|---|---|
| 40% off $20 | $12 | $8 |
| 20% off $40 | $32 | $8 |
| 30% off $60 | $42 | $18 |
| 60% off $30 | $12 | $18 |
| 25% off $20 | $15 | $5 |
| 20% off $50 | $40 | $10 |
| 15% off $80 | $68 | $12 |
| 35% off $100 | $65 | $35 |
Undoing a discount: the markup back to full price
A discount and a price rise of the same percentage don't cancel out. After 20% off, a 20% rise takes $100 to only $96. This matters when a sale ends, or when a retailer sets a price by marking up cost: the increase needed to return to the original is sale-price-based, so it is always larger than the discount.
| Discount | Increase to undo it |
|---|---|
| 10% off | +11.1% |
| 20% off | +25% |
| 25% off | +33.3% |
| 30% off | +42.9% |
| 40% off | +66.7% |
| 50% off | +100% |
| 75% off | +300% |
Stacked discounts: why 20% + 10% isn't 30%
"Take an extra 10% off sale prices" means 10% off the already-reduced price. The combined discount is always less than the sum. The table shows the total discount and what a $100 item ends up costing.
| First discount | Then | Total discount | $100 item costs |
|---|---|---|---|
| 20% | 10% | 28% | $72 |
| 20% | 20% | 36% | $64 |
| 25% | 10% | 32.5% | $67.50 |
| 30% | 10% | 37% | $63 |
| 30% | 20% | 44% | $56 |
| 40% | 10% | 46% | $54 |
| 40% | 20% | 52% | $48 |
| 50% | 10% | 55% | $45 |
| 50% | 20% | 60% | $40 |
| 50% | 50% | 75% | $25 |
Order doesn't matter for two percentage discounts: 10% then 20% gives the same $72. It does matter when one is a dollar amount: $10 off then 20% off $100 is $72, while 20% off then $10 off is $70.
Original price from sale price
What an item cost before the discount, given what you paid (sale price ÷ (1 − discount)).
| You paid | after 20% off, was | after 25% off, was | after 30% off, was | after 40% off, was | after 50% off, was |
|---|---|---|---|---|---|
| $10 | $12.50 | $13.33 | $14.29 | $16.67 | $20 |
| $20 | $25 | $26.67 | $28.57 | $33.33 | $40 |
| $25 | $31.25 | $33.33 | $35.71 | $41.67 | $50 |
| $30 | $37.50 | $40 | $42.86 | $50 | $60 |
| $36 | $45 | $48 | $51.43 | $60 | $72 |
| $50 | $62.50 | $66.67 | $71.43 | $83.33 | $100 |
| $75 | $93.75 | $100 | $107.14 | $125 | $150 |
| $100 | $125 | $133.33 | $142.86 | $166.67 | $200 |
Don't add the percent back on: $36 plus 40% is $50.40, not the original $60.
Sales tax on discounted items
The calculator adds tax to the sale price. That matches how New York treats a store's own discount: its tax department says that because the seller isn't reimbursed for a store coupon, "tax is calculated on the reduced price." A manufacturer's coupon is different: New York says sales tax is due on the full price, because the manufacturer pays the store back. California's CDTFA Publication 113 draws the same line between discounts the retailer absorbs and ones a third party reimburses. For example, $60 at 40% off with 8% tax is $36 + $2.88 tax = $38.88. Rates and rules vary by state and city, so enter your local rate.
Is the "original price" real?
A percent off is only as honest as the price it starts from. The FTC's Guides Against Deceptive Pricing say a former-price comparison is legitimate when 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" (16 CFR § 233.1(a)). A price inflated just so it can be "cut" makes the bargain false. The guides also warn that a tiny cut, such as "reduced to $9.99" from $10, misleads shoppers who expect a real saving (§ 233.1(e)). Comparing prices at other stores before you buy is the best check.
"Compare at" and "list price" tags follow similar rules. A retailer comparing its price with other stores' should be reasonably certain the higher price doesn't appreciably exceed what substantial sales in its trade area are made at (§ 233.2). A manufacturer's suggested price is fair only if a substantial number of sales happen at that price in the area (§ 233.3). The guides say that today "only in the rare case" are all sales of an article made at the list price. So treat a percent off MSRP as an upper bound on your real saving.
Common mistakes
- Adding stacked discounts. 50% off plus 50% off is 75% off, not free.
- Reversing a discount by adding the percent back. Divide by (1 − %) instead.
- Confusing "40 off" with $40 off. In a sale, "40 off" nearly always means 40 percent. $40 off $60 would be $20.
- Forgetting tax. Add your local sales tax rate to see what you'll actually pay.
The same percentage maths works elsewhere: the percentage calculator finds any percent of a number, the tip calculator adds a percentage instead of taking one off, the pay raise calculator applies it to a salary, and the grade calculator turns test scores into percentages. Splitting a month's rent by days uses the same proportional arithmetic in the prorated rent calculator.
Frequently asked questions
How do you calculate a discount?
Multiply the original price by the discount rate to get the amount of discount, then subtract it from the original price. OpenStax Prealgebra's example: a $140 dress at 35% off has a discount of 0.35 × $140 = $49 and a sale price of $91.
What is 40 off of 25?
40% off $25 is $15. The discount is 0.40 × $25 = $10, and $25 − $10 = $15. If the tag means $40 off a $25 item, that would be more than the price, so it is almost certainly 40 percent.
What is a discount computation?
It is the two-line calculation a till or invoice does: discount = price × rate, then net price = price − discount. For $79.99 at 15% off: discount $12, net price $67.99. The calculator does the same and can add an extra discount, a coupon and tax.
How do you calculate percent off?
Multiply the price by (1 − percent ÷ 100). For 40% off $60: $60 × 0.60 = $36. The savings are price × percent ÷ 100: $60 × 0.40 = $24. Working with the percentage you keep (60%) is one step instead of two, and avoids subtracting the wrong number.
How do I work out what percent off I got?
Divide the sale price by the original price, subtract from 1 and multiply by 100. Paying $36 for a $60 item is (1 − 36 ÷ 60) × 100 = 40% off. Useful when a tag shows only "was" and "now" prices.
Is buy one, get one 50% off the same as 25% off?
On two items of the same price, yes: you pay 1.5 prices for 2 items, which is 25% off each. Two $40 items cost $40 + $20 = $60, the same as 25% off $80. If the prices differ, the half-off usually applies to the cheaper item, so the overall saving is less than 25%.
How do I find the original price from the sale price?
Divide the sale price by (1 − percent ÷ 100). If you paid $36 after 40% off, the original price was $36 ÷ 0.60 = $60.
Is sales tax charged on the sale price or the original price?
For a store's own discount, on the reduced price in states such as New York: its tax department says tax is calculated on the reduced price because the seller isn't reimbursed. With a manufacturer's coupon, New York taxes the full price, because the manufacturer reimburses the store. Rules vary by state.
What is 20 percent off 50?
$50 × 0.80 = $40. You save $10. The shortcut: 10% of $50 is $5, so 20% is $10.
What is 40% off $20, and 20% off $40?
40% off $20 is $20 × 0.60 = $12. 20% off $40 is $40 × 0.80 = $32. The dollar savings are the same ($8) because 40% of 20 equals 20% of 40, but the prices you pay differ.
How much is buy two, get one free as a percent off?
You pay for 2 items and take 3 home, so each costs two thirds of its price: 33.3% off when all three cost the same. Buy one, get one free is 50% off, and buy three, get one free is 25% off.
How much do I need to mark a price back up after a discount?
More than the discount. After 40% off, you need a 66.7% increase to return to the original price, because the increase is measured on the smaller sale price. After 50% off you need +100%.
Sources & method
- FTC Guides Against Deceptive Pricing, 16 CFR Part 233 (eCFR) — former-price comparisons, § 233.1
- OpenStax Prealgebra 2e, §6.3 Solve Sales Tax, Commission, and Discount Applications — amount of discount and sale price
- New York State Dept. of Taxation and Finance — Coupons (tax on store-discounted vs manufacturer-coupon prices)
- California CDTFA Publication 113 — Coupons, Discounts, and Rebates
- FTC Guide Concerning Use of the Word "Free", 16 CFR § 251.1 (eCFR) — Buy 1-Get 1 Free, regular price, frequency of offers
Results are estimates for general information. Found an error? It helps everyone — see our methodology.