How to Find the Original Price Before a Discount
The reverse discount formula — work backwards from the sale price to find what something originally cost, with step-by-step examples and a full reference table.
The Reverse Discount Formula Explained
When a discount is applied, the sale price is a fraction of the original. A 30% discount means you pay 70% of the original — so the sale price equals the original price multiplied by 0.70. To go backwards, you divide instead of multiply.
The general formula is: Original Price = Sale Price ÷ (1 − Discount% ÷ 100). The expression (1 − Discount% ÷ 100) is called the "keep factor" — the proportion of the original price that remains after the discount. For 30% off, the keep factor is 0.70. For 25% off, it's 0.75. For 50% off, it's 0.50.
Dividing the sale price by the keep factor reverses the multiplication that created it. It is the mathematical inverse of calculating percent off.
Worked Example: 30% Off, Sale Price $63
The Most Common Mistake: Adding the Percentage Back
A common error is trying to reverse a 30% discount by adding 30% to the sale price: $63 × 1.30 = $81.90. This gives the wrong answer.
Why? Because the 30% was taken off the original price ($90), not the sale price ($63). When you add 30% back to the sale price, you're calculating 30% of the wrong base — a smaller number — so the result is always too low.
The correct answer is $90, not $81.90. The only reliable way to reverse a discount is division by the keep factor.
This mistake is surprisingly common, even in retail contexts. If you see a "pre-sale price" that was calculated by adding a discount percentage back to the sale price, it will always be understated by a meaningful margin.
Quick Reference: Keep Factors by Discount Rate
Every discount rate has a corresponding keep factor. Memorising a handful of them makes reverse calculations much faster.
| Discount | Keep Factor | Shortcut to Reverse | Example: Sale $60 → Original |
|---|---|---|---|
| 5% off | 0.95 | ÷ 0.95 | $60 ÷ 0.95 = $63.16 |
| 10% off | 0.90 | ÷ 0.90 | $60 ÷ 0.90 = $66.67 |
| 15% off | 0.85 | ÷ 0.85 | $60 ÷ 0.85 = $70.59 |
| 20% off | 0.80 | ÷ 0.80 | $60 ÷ 0.80 = $75.00 |
| 25% off | 0.75 | ÷ 0.75 (×4÷3) | $60 ÷ 0.75 = $80.00 |
| 30% off | 0.70 | ÷ 0.70 | $60 ÷ 0.70 = $85.71 |
| 33% off | 0.67 | ÷ 0.67 | $60 ÷ 0.67 = $89.55 |
| 40% off | 0.60 | ÷ 0.60 (×5÷3) | $60 ÷ 0.60 = $100.00 |
| 50% off | 0.50 | ÷ 0.50 (×2) | $60 ÷ 0.50 = $120.00 |
| 60% off | 0.40 | ÷ 0.40 (×2.5) | $60 ÷ 0.40 = $150.00 |
| 70% off | 0.30 | ÷ 0.30 | $60 ÷ 0.30 = $200.00 |
| 75% off | 0.25 | ÷ 0.25 (×4) | $60 ÷ 0.25 = $240.00 |
| 80% off | 0.20 | ÷ 0.20 (×5) | $60 ÷ 0.20 = $300.00 |
Need the sale price instead?
Use the Discount Calculator to go the other direction — enter the original price and get the discounted amount instantly.
Full Reference Table: Sale Price × Discount → Original Price
This table shows the original price for a range of sale prices and discount rates. All values are rounded to the nearest cent. Use it to quickly reverse any common discount scenario.
| Sale Price | 10% off | 20% off | 25% off | 30% off | 40% off | 50% off |
|---|---|---|---|---|---|---|
| $9 | $10.00 | $11.25 | $12.00 | $12.86 | $15.00 | $18.00 |
| $18 | $20.00 | $22.50 | $24.00 | $25.71 | $30.00 | $36.00 |
| $27 | $30.00 | $33.75 | $36.00 | $38.57 | $45.00 | $54.00 |
| $36 | $40.00 | $45.00 | $48.00 | $51.43 | $60.00 | $72.00 |
| $45 | $50.00 | $56.25 | $60.00 | $64.29 | $75.00 | $90.00 |
| $54 | $60.00 | $67.50 | $72.00 | $77.14 | $90.00 | $108.00 |
| $63 | $70.00 | $78.75 | $84.00 | $90.00 | $105.00 | $126.00 |
| $72 | $80.00 | $90.00 | $96.00 | $102.86 | $120.00 | $144.00 |
| $80 | $88.89 | $100.00 | $106.67 | $114.29 | $133.33 | $160.00 |
| $90 | $100.00 | $112.50 | $120.00 | $128.57 | $150.00 | $180.00 |
| $100 | $111.11 | $125.00 | $133.33 | $142.86 | $166.67 | $200.00 |
| $120 | $133.33 | $150.00 | $160.00 | $171.43 | $200.00 | $240.00 |
| $150 | $166.67 | $187.50 | $200.00 | $214.29 | $250.00 | $300.00 |
| $180 | $200.00 | $225.00 | $240.00 | $257.14 | $300.00 | $360.00 |
| $200 | $222.22 | $250.00 | $266.67 | $285.71 | $333.33 | $400.00 |
| $240 | $266.67 | $300.00 | $320.00 | $342.86 | $400.00 | $480.00 |
| $300 | $333.33 | $375.00 | $400.00 | $428.57 | $500.00 | $600.00 |
When You Only Know the Savings Amount
Sometimes you know how much money you saved and the discount rate, but not the original price. In that case, the formula is even simpler: Original Price = Savings ÷ (Discount% ÷ 100). If you saved $18 on a 30% off sale, the original price was $18 ÷ 0.30 = $60. The sale price was $60 − $18 = $42.
This formula is a useful secondary check. If a store tells you that you saved a certain dollar amount, you can immediately verify whether the claimed percentage is consistent with their advertised original price.
Working Backwards Through Stacked Discounts
When multiple discounts have been applied in sequence — common in clearance sales or with stacked coupon codes — you must reverse them one at a time, starting from the last discount applied and working backwards. This is the inverse of how stacked discounts compound.
Example: a final price of $54 after first a 25% discount, then an additional 10% off. To find the original:
Trying to add 35% (25% + 10%) back to $54 gives $72.90 — wrong on two counts. First, you can't add stacked discount rates. Second, you can't add the percentage back at all. Always reverse each discount individually by dividing.
Reverse Discount vs Reverse Markup: What's the Difference?
Both reverse a multiplication, but the direction of the original operation differs. Understanding when to use which formula matters if you work in retail, purchasing, or accounting.
Reverse a Discount
A discount reduces the original price. A 25% discount means the seller charged 75% of their original price.
Original = Sale Price ÷ (1 − 0.25)
= Sale Price ÷ 0.75
Use when: you know what a customer paid and you want to know the pre-discount list price.
Reverse a Markup
A markup increases a cost price. A 25% markup means the seller charged 125% of their cost.
Cost = Selling Price ÷ (1 + 0.25)
= Selling Price ÷ 1.25
Use when: you know a retail price and want to estimate the underlying cost given a typical markup percentage.
The formulas look parallel, but notice that reversing a discount uses 1 minus the rate, while reversing a markup uses 1 plus the rate. Confusing the two is a common accounting error that produces systematically incorrect cost or price estimates.
Using the Reverse Formula to Spot Inflated "Original" Prices
One practical use for this formula is verifying retailer claims. Many retailers inflate their "original" or "compare at" prices, then advertise steep discounts off the inflated number. If a store claims a jacket that now sells for $63 originally cost $81.90 (arrived at by adding 30% to $63), you can immediately identify the error: the genuine original price implied by a 30% discount and a sale price of $63 is $90, not $81.90.
Price tracking tools can help verify whether an "original" price was ever actually charged, but the math alone can sometimes reveal when the arithmetic doesn't add up. If the claimed savings percentage produces an original price by the correct formula that doesn't match what the store claims, at least one of the numbers is wrong.
For a deeper look at what a percentage discount actually means and how to evaluate deals, see what percent off means in practice. For calculating the sale price from the original price, the percent off calculator handles that direction directly.
The Formula in Everyday Contexts
The reverse discount calculation comes up in a wider range of situations than pure shopping. In payroll and HR, if an employee's net-of-deduction take-home is known, the same algebraic structure recovers the gross pay given a deduction rate. In tax work, removing VAT from a tax-inclusive price is identical in structure: divide by (1 + VAT rate) instead of (1 − discount rate), because VAT adds to the base price rather than subtracting from it.
In each case, the underlying logic is the same. You know a final value that was produced by multiplying a starting value by some factor. Division by that factor recovers the original. The only variation is whether the factor is greater than one (markup, VAT) or less than one (discount), and whether it was applied to the original or the sale value.
For percentage changes more broadly — including situations where a value increased rather than decreased — the percentage change calculator can handle both directions.
Mental Math Shortcuts for Common Discounts
A few discount rates have particularly clean reversal shortcuts that are worth knowing for quick, in-the-field estimates.
50% off: Multiply the sale price by 2. A $30 sale price → $60 original. This is exact.
25% off: Multiply by 4 and divide by 3 (or simply multiply by 1.333…). A $75 sale price → $75 × 4 ÷ 3 = $100. Alternatively, $75 ÷ 0.75 = $100. This is exact.
20% off: Divide by 0.8, or equivalently multiply by 1.25. A $80 sale price → $80 × 1.25 = $100. This is exact.
10% off: Divide by 0.9. A $45 sale price → $45 ÷ 0.9 = $50. A useful approximation: the original is about 11.1% more than the sale price.
33% off (one-third off): Divide by 0.667, or multiply by 1.5. A $40 sale price → $40 × 1.5 = $60. This works because a one-third reduction leaves two-thirds, and dividing by 2/3 is the same as multiplying by 3/2 = 1.5.