How to use the discount calculator
- Choose what you want to work out. The usual case is a percent off a price. You can also take a dollar amount off, stack two percentage discounts, find the percent off from an original and a sale price, or find the original price behind a sale price.
- Enter the prices and discounts. The chips fill in common percentages.
- Optional: add sales tax. Enter your local rate to see the total at the register. Tax is charged on the discounted price.
The results show the sale price, the dollars saved, the share of the original you are paying and the total with tax, so you can compare offers quickly in a store or online.
Discount formulas
Sale price = original price − discount = original × (1 − rate)
Percent off = (original − sale) ÷ original × 100
Original price = sale price ÷ (1 − rate)
Total = sale price × (1 + tax rate)
Worked example from a textbook. OpenStax’s Prealgebra 2e (section 6.3) prices a dress at $140 with 35% off. The discount is 0.35 × $140 = $49, and the sale price is $140 − $49 = $91. The same answer comes from one multiplication: you pay 65% of the price, and 0.65 × $140 = $91.
For a fixed dollar discount, subtract it directly. The textbook’s sunglasses cost $39 with $10 off, so they sell for $29, which works out to about 25.6% off.
Stacked discounts: why 20% + 10% is not 30%
“Take an extra 10% off sale prices” means the second discount applies to the already-reduced price, not the original. On a $50 item marked 20% off, the sale price is $40. An extra 10% off $40 is $4, leaving $36. The total discount is $14, which is 28% of $50, not 30%.
| First discount | Extra discount | Combined | $100 item costs |
|---|---|---|---|
| 20% | 10% | 28% | $72.00 |
| 25% | 15% | 36.25% | $63.75 |
| 30% | 20% | 44% | $56.00 |
| 40% | 25% | 55% | $45.00 |
| 50% | 50% | 75% | $25.00 |
The order does not matter: 10% then 20% gives the same 28%. What matters is whether the second discount is on the sale price (stacked) or on the original price (added). If a store says the discounts are added, simply add the percentages and use the percent-off mode.
Finding the percent off or the original price
Percent off from two prices. Subtract the sale price from the original and divide by the original. A jacket marked down from $80 to $60 is $20 off, and $20 ÷ $80 = 25% off. Divide by the original price, not the sale price: $20 ÷ $60 would suggest 33%, which overstates the deal.
Original price from a sale price. If a tag shows only “$60, 25% off,” the original price is $60 ÷ (1 − 0.25) = $60 ÷ 0.75 = $80. Adding 25% back to $60 gives $75, which is wrong, because the 25% was taken from the larger original price.
This reverse calculation is useful for checking whether a “was” price is believable. The Federal Trade Commission’s guides on former price comparisons (16 CFR 233.1) say a former price is a fair basis for a discount claim only if the item was openly offered at that price for a reasonably substantial period. If an item seems to be on permanent sale, compare the sale price with other stores rather than with the reference price.
Discounts and sales tax
Sales tax is a percentage of the purchase price, so it applies after the discount in most cases. OpenStax’s section 6.3 shows the tax step on its own: a $392 bicycle at a 6.5% rate carries $25.48 in tax, for a total of $417.48. Combined with a discount, take the discount first and then add tax on the reduced price. The dress from the formula example, $91 after 35% off, costs $91 × 1.065 = $96.92 with 6.5% tax.
Store coupons and manufacturer coupons can be taxed differently, and rates vary by city and state. If the receipt does not match, the usual reason is that tax was charged on a different base. The calculator’s tax field is for estimating; it does not look up local rates.
Quick mental math for common discounts
A few shortcuts cover most price tags. For 10% off, move the decimal point one place left and subtract: 10% of $64 is $6.40, so $57.60. For 20%, double the 10% figure. For 25%, take a quarter of the price. For 30%, triple the 10% figure. For 15%, add the 10% figure to half of itself: 10% of $40 is $4, half of that is $2, so 15% is $6 off, a $34 price.
Another approach is to think about what you pay rather than what you save. At 35% off you pay 65%; at 40% off you pay 60%. Multiplying the original price by that share gives the sale price in one step, which is how the calculator does it.
Comparing offers: percent off, dollars off and multi-buy deals
When a store offers a choice, such as 20% off or $15 off, the better deal depends on the price. The two are equal where 20% of the price is $15, which is at $75. Below $75 the dollar coupon saves more; above it the percentage does. In general, a dollar discount beats a percentage discount when the price is less than the dollar amount ÷ the rate.
Multi-buy offers can be turned into a percent off too. “Buy two, get one free” on equal-priced items means paying for two out of three, a 33.3% discount on the three. “Buy one, get one 50% off” is paying for 1.5 out of 2, a 25% discount. These only save money if you wanted the extra items anyway.
For a fair comparison between stores, compare final prices with tax and shipping rather than headline percentages. A 40% discount on an inflated reference price can cost more than a 15% discount somewhere else.
Sources & assumptions
How this calculator gets its numbers. Full method: our methodology.
- Sale price = original × (1 − discount %). Dollars off are subtracted from the original price.
- Stacked discounts apply one after the other, so the combined discount is 1 − (1 − first) × (1 − second).
- Original price from a sale price = sale price ÷ (1 − discount %).
- Sales tax, if entered, is charged on the discounted price. Coupons that a store treats differently for tax are not modeled.
- Amounts are shown to the cent; a store may round each step.
Sources
- OpenStax (Rice University), Prealgebra 2e, 6.3 Solve Sales Tax, Commission, and Discount Applications. Commission = rate × total sales (3% on a $260,000 house is $7,800; $87 on a $1,450 stove is 6%), discount = rate × original price (35% off $140 is $49, a $91 sale price), and sales tax as a percent of the purchase price.
- Federal Trade Commission (eCFR), 16 CFR 233.1, Former price comparisons. A “was” price is only a fair basis for a discount if the item was openly offered at that price for a reasonably substantial period.
Last reviewed . Check the receipt: store policies decide how coupons, bundles and tax combine.
Frequently asked questions
How do I calculate a discount?
Multiply the original price by the discount rate written as a decimal, then subtract the result from the original price. For 30% off $70: 0.30 × $70 = $21 off, so the sale price is $49.
How do I find the percent off?
Subtract the sale price from the original price and divide by the original price, then multiply by 100. From $120 to $90 is $30 off, and $30 ÷ $120 = 0.25, or 25% off.
Is 20% off plus an extra 10% off the same as 30% off?
No. The extra 10% is taken from the already-reduced price, so the combined discount is 1 − 0.8 × 0.9 = 28%. On a $100 item, you pay $72 instead of $70.
How do I find the original price before a discount?
Divide the sale price by one minus the discount rate. A $45 item that is 40% off had an original price of $45 ÷ 0.60 = $75.
Is sales tax calculated before or after a discount?
Usually after: tax is charged on the price you actually pay. A $100 item at 20% off with 8% tax costs $80 × 1.08 = $86.40. Some coupon types are treated differently by state tax rules, so check the receipt.
What is 25% off $60?
25% of $60 is $15, so the sale price is $45. Since 25% is one quarter, you can also divide $60 by 4 to get the discount.