How to recover the original price from a discounted price
Reverse a discount by dividing by the proportion of price that remains. Adding the same percentage to the sale price generally does not restore the original amount.
Discount calculator →Write the relationship before reversing it
Sale price equals original price multiplied by one minus the discount rate. Therefore original price equals sale price divided by one minus that rate. This reversal requires a discount below 100%. If an item is free after a complete discount, a zero sale price alone cannot reveal what the original price was.
Recover a price after twenty percent off
If the sale price is 80 after a 20% discount, the original price is 80/0.8 = 100. Adding 20% to 80 instead gives only 96. The reduction originally used 100 as its base, whereas that attempted increase uses 80. The monetary saving is 20, and the direction of the percentage calculation determines which base belongs in the denominator.
Verify with the forward calculation
The discount tool primarily calculates forward from original price. Use the scientific calculator for the reverse division, then enter the inferred original price and discount into the discount tool to check the result. If the paid amount also contains shipping, a fixed coupon or a tax adjustment, one percentage may not recover a meaningful list price. Whether an advertised original price is genuine is a separate question from whether the arithmetic is consistent.
Try the calculators
- Discount calculator
Find the sale price and how much you save.
- Percentage calculator
Find a percentage of any number.
- Profit margin and markup calculator
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