To find the original price from a sale price, divide the sale price by (1 minus the discount as a decimal): original price = sale price ÷ (1 − discount rate). For example, an item marked $59.99 after 25% off had an original price of $79.99, because $59.99 ÷ (1 − 0.25) = $59.99 ÷ 0.75 = $79.99. The key trick is that you divide, not multiply, and you never add the percentage back to the sale price.
This is the math that confuses almost every shopper. Adding 25% to a $59.99 price gives $74.99, which is wrong. You have to undo the discount, not apply a fresh one. This guide shows the reverse-discount formula, a copy-and-paste table for the most common percent-off deals, how to work backward when you only know the dollars you saved, and how to handle sales tax. Plug any numbers into our discount calculator to skip the arithmetic.
Why you cannot just add the percentage back
A discount is taken off the original price, so the percentage is measured against a number you do not have yet. When a store takes 25% off, the shopper pays 75% of the original. The sale price is 75% of the original, so to get back to 100% you divide by 0.75, not multiply by 1.25.
Here is the trap in numbers. Suppose the original was $100 and the store takes 25% off, leaving a $75 sale price. If you tried to recover the original by adding 25% to $75, you would get $93.75, not $100. That is because 25% of $75 ($18.75) is smaller than 25% of $100 ($25). The percentage shrinks when the base shrinks, which is exactly why reversing a discount requires division.
The reverse-discount formula
The formula to recover the original price has just three pieces:
Original price = Sale price ÷ (1 − discount rate)
- Sale price is the marked-down price you see on the tag.
- Discount rate is the percent off written as a decimal: 25% becomes 0.25, 40% becomes 0.40.
- (1 − discount rate) is the fraction of the original you actually pay. At 25% off you pay 0.75 of the original.
Three worked examples:
- $42.00 after 30% off: $42.00 ÷ (1 − 0.30) = $42.00 ÷ 0.70 = $60.00 original.
- $63.74 after 15% off: $63.74 ÷ 0.85 = $74.99 original.
- $89.25 after 15% off: $89.25 ÷ 0.85 = $105.00 original.
For the everyday version of this calculation, our percentage calculator handles any "X is what percent of Y" question, while the discount calculator does sale price, savings, and original price in one step.
Step-by-step: reverse a single discount
Follow these steps to recover the original price from any single percent-off sale.
- Write the discount as a decimal. Move the percent two places left: 25% becomes 0.25, 40% becomes 0.40, 7% becomes 0.07.
- Subtract it from 1. This gives the fraction you actually pay. At 25% off, 1 − 0.25 = 0.75.
- Divide the sale price by that number. $59.99 ÷ 0.75 = $79.99.
- Round to the cent. Prices almost always come out to a clean tag price like $79.99 or $105.00, which is a good sign you did it right.
- Sanity check. Your original should always be larger than the sale price. If it is smaller, you multiplied instead of dividing.
Quick-reference table: original price by percent off
This table shows the original price for a $50 sale tag at common discount levels. The pattern is the same for any sale price: divide by the "you pay" fraction.
| Percent off | You pay (fraction) | Divide $50 by | Original price |
|---|---|---|---|
| 10% | 0.90 | 0.90 | $55.56 |
| 20% | 0.80 | 0.80 | $62.50 |
| 25% | 0.75 | 0.75 | $66.67 |
| 30% | 0.70 | 0.70 | $71.43 |
| 40% | 0.60 | 0.60 | $83.33 |
| 50% | 0.50 | 0.50 | $100.00 |
| 70% | 0.30 | 0.30 | $166.67 |
Notice that at 50% off the original is exactly double the sale price, and at 70% off it is more than triple. The deeper the discount, the larger the multiplier needed to get back to the original.
Working backward from the dollars you saved
If you know the dollar amount you saved and the percent off, the original price is the savings divided by the discount rate. The formula is original price = savings ÷ discount rate.
Example: a sign says "Save $12, today only 30% off." The original price was $12.00 ÷ 0.30 = $40.00, and the sale price is $40.00 − $12.00 = $28.00. This is useful when a store advertises the dollars-off and the percent but hides the starting price.
You can also go the other way: if you know the original and the sale price but not the percent, the discount rate is (original − sale) ÷ original. A $120 item now selling for $90 is ($120 − $90) ÷ $120 = $30 ÷ $120 = 0.25, or 25% off.
Reversing a stacked discount
To reverse two stacked discounts, divide by each "you pay" fraction, because stacked percents multiply rather than add. A 20% coupon on top of a 10% sale leaves you paying 0.90 × 0.80 = 0.72 of the original, which is 28% off in total, not 30%.
So if you paid $42.00 after a 10% sale and an extra 20% off, the original was $42.00 ÷ (0.90 × 0.80) = $42.00 ÷ 0.72 = $58.33. The order of the two discounts does not change the answer, because multiplication is order-independent: 0.90 × 0.80 equals 0.80 × 0.90.
Reversing a discount when sales tax is on the receipt
If your only number is the final receipt total including tax, strip out the tax first, then reverse the discount. Sales tax is applied after the discount in almost every US state, so it sits on the outside of the calculation.
Example: your receipt shows $64.80 for one item, the local sales tax is 8%, and the item was 20% off. First remove the tax: $64.80 ÷ 1.08 = $60.00 pre-tax sale price. Then reverse the discount: $60.00 ÷ 0.80 = $75.00 original. If you skipped the tax step you would have overstated the original price. For the tax side of any purchase, our sales tax calculator backs the tax out of a total in one step.
Common mistakes when reversing a discount
- Adding the percentage back instead of dividing. Adding 25% to a sale price always lands short of the true original. Always divide by (1 − rate).
- Forgetting that stacked discounts multiply. Reversing "30% off" when the deal was really 20% then 10% (28% off) gives the wrong original.
- Reversing before removing tax. Tax goes on after the discount, so peel it off first.
- Mixing up percent off and percent paid. 40% off means you pay 60%. Divide by 0.60, not 0.40.
Where this math shows up beyond shopping
The reverse-discount formula is the same "undo a percentage" logic that powers several money calculations. Backing a pre-tax figure out of a tax-inclusive total uses the same division, as does finding a pre-raise salary from a post-raise paycheck with our pay raise calculator. Recovering an original investment value before a percentage gain is the present-value cousin handled by the present value calculator. And comparing two deals by their true per-unit cost is exactly what our unit price calculator is built for. If you want the deeper percentage-change mechanics, the pay raise percentage guide walks through the same reverse-percent reasoning.
For a plain-English refresher on what percentages actually represent, the U.S. Federal Trade Commission's consumer pages on comparison shopping and pricing are a reliable, neutral reference.
The bottom line
Recovering an original price is one short division: take the sale price and divide it by the fraction you actually paid. At 25% off you divide by 0.75, at 40% off you divide by 0.60, and for stacked deals you divide by the product of each fraction. The only real mistake is adding the percentage back, which always undershoots. Memorize "divide, do not add" and you can verify any "was/now" tag in seconds.
Try it yourself
Enter a sale price and percent off to recover the original instantly in the free Discount Calculator — no sign-up.
Open the Discount Calculator →Try it yourself
Run your own numbers in the free Discount Calculator — instant, private, no sign-up.
Open the Discount Calculator →Frequently asked questions
- How do I find the original price from a sale price?
- Divide the sale price by (1 minus the discount as a decimal). For a $59.99 price after 25% off, that is $59.99 / 0.75 = $79.99. Never add the percentage back to the sale price, because that always undershoots the true original.
- Why can't I just add the discount percentage back to the sale price?
- Because the discount was measured against the original, not the sale price. A 25% discount on a $100 item gives $75, but adding 25% to $75 gives only $93.75, not $100. The percentage shrinks when the base shrinks, so you must divide instead of add.
- What is the formula to reverse a discount?
- The formula is original price = sale price / (1 - discount rate). Write the percent off as a decimal, subtract it from 1 to get the fraction you pay, then divide the sale price by that fraction. At 40% off you divide by 0.60.
- How do I find the original price if I only know how much I saved?
- Divide the dollar savings by the discount rate. If you saved $12 on a 30%-off deal, the original was $12 / 0.30 = $40.00, and the sale price was $40.00 - $12.00 = $28.00.
- How do I work out the discount percentage from the original and sale price?
- Subtract the sale price from the original, then divide by the original. A $120 item now $90 is ($120 - $90) / $120 = $30 / $120 = 0.25, or 25% off.
- How do I reverse two stacked discounts?
- Divide by the product of each fraction you pay, because stacked discounts multiply. After a 10% sale and an extra 20% off you pay 0.90 x 0.80 = 0.72 of the original, so $42 / 0.72 = $58.33. The order of the two discounts does not change the answer.
- Do I remove sales tax before reversing a discount?
- Yes. Tax is added after the discount in almost every US state, so strip it out first. A $64.80 tax-inclusive total at 8% tax is $64.80 / 1.08 = $60.00 pre-tax, and if the item was 20% off the original was $60.00 / 0.80 = $75.00.
- At 50% off, is the original price exactly double the sale price?
- Yes. At 50% off you pay half the original, so dividing the sale price by 0.50 doubles it. A $100 sale tag started at $200. At 70% off the original is more than triple the sale price, because you divide by 0.30.
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