Original Price from a Sale
Work back from a discounted price and the discount rate to the original.
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Formula
How the calculation works
This runs a discount backwards, and backwards means dividing. A 2,040 price at 15% off came from 2,040 divided by 0.85, which is 2,400. The 360 difference is the saving, and it is 15% of 2,400 and not of 2,040, which is exactly why adding 15% to the sale price gives 2,346 and misses by 54.
The smaller the remaining fraction, the more violent the reverse. At 50% off the divide is by 0.5, so a 100 sale price doubles to a 200 original. At 90% off it divides by 0.1, so the same 100 came from 1,000. That is why a deep-discount tag hides a far bigger original than intuition suggests, and why the addition method goes badly wrong as the rate climbs.
The rate must stay under 100%, and the code refuses 100% outright rather than returning infinity. The forward tool and this one are exact inverses, so a 2,040 price at 15% off returns to 2,400 and then forward again to 2,040, with no drift from the round trip. That check is what makes a claimed saving verifiable.
Common mistakes
- Adding the discount to the sale price. At 15% off, 2,040 plus 15% is 2,346, while the true original is 2,400; the error is 54 and it grows with the rate.
- Dividing by the discount rate instead of the fraction kept. Dividing 2,040 by 15 gives 136, which is not a price of anything.
- Trusting a tag that claims 100% off. There is no price to recover there, and the tool refuses the input rather than inventing one.
When to use it
- Use it when you have the sale price and the discount rate and want to know whether a claimed saving is real, or to check a price history before buying something you will resell.
- If you have the original price and want the sale price instead, use the discount calculator; the two directions look alike and are not interchangeable.
Worked example
A 2,040 sale price at 15% off means the original was 2,400.
Common questions
Why is adding 15% to 2,040 wrong?
Because the 15% came off 2,400, not off 2,040. You must divide, not add; the two differ by about 36.
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