Recover an original amount after a known percentage reduction. Enter the two values below. The result panel shows the calculation used, and the examples explain how to interpret it.
How to use the reverse percentage calculator
- Identify the values required by the input labels.
- Enter percentages as whole-number rates: 15 means 15%.
- Select Calculate and read the result together with its formula.
- Check the assumptions below before applying the answer to a real situation.
Formula and method
Worked example
An item costs 72 after a 20% discount. The final price represents 80% of the original, not 100%. Divide 72 by 0.80 to get 90. Check it by taking 20% of 90, which is 18, then subtracting 18 to return to 72.
Adding 20% to 72 gives 86.40, so it does not reverse the discount. That calculation uses the reduced price as its base. Reverse percentages instead recover the missing original base by division.
Reverse an increase instead
This interactive tool reverses a discount. To reverse an increase of p%, use original = final ÷ (1 + p ÷ 100). If a total of 120 includes a simple 20% increase, divide by 1.20 to get 100. Do not use the discount mode for that different question.
Example calculations
| Sale price | Discount | Original price |
|---|---|---|
| 80 | 20% | 100 |
| 63 | 30% | 90 |
| 45 | 25% | 60 |
| 120 | 0% | 120 |
Input rules and limitations
Discounts must be at least 0% and below 100%. A final value after a 100% discount is zero regardless of the original price, so a unique original cannot be recovered.
Display precision can be changed from two to eight decimal places. Intermediate values are not rounded, but the calculation uses standard browser floating-point arithmetic. Currency figures should be rounded according to the rules relevant to your actual transaction.
Common questions
Does the result include units?
The calculator works with numbers. Keep the same units for comparable quantities and add the appropriate unit when reporting the result.
Why does the calculator reject some inputs?
Discounts must be at least 0% and below 100%. A final value after a 100% discount is zero regardless of the original price, so a unique original cannot be recovered.
Is my information sent to a server?
Calculator values stay in your browser. They are not submitted to the website’s server for calculation.
Where can I learn the related formulas?
Use the main percentage calculator for basic shares and wholes, or browse our guides for worked examples and common mistakes.
Choose the right comparison
Use the percentage change calculator for an original-to-new comparison, the percentage difference calculator when neither value is the baseline, and the percentage points calculator to subtract rates. You can also return to the main percentage calculator.