Reverse Percentage Calculator
Find the original amount before a percentage increase or decrease, with the inverse formula explained.
Enter Known Values
Recovered original amount
100
80 ÷ (1 − 20 ÷ 100)- Percentage multiplier
- 0.8
- Forward check
- 80
How does a reverse percentage find the original amount?
A reverse percentage finds the starting value from a known final value and rate. Divide the final value by 1 plus the increase rate, or by 1 minus the decrease rate, after converting the percentage to a decimal.
Key Takeaways
- Enter the known final amount after the percentage was applied.
- Enter the percentage rate and choose increase or decrease.
- Read the recovered original value, multiplier, and forward check.
How does a reverse percentage find the original amount?
Forward percentage calculations multiply an original value by a percentage multiplier. Reverse calculations undo that operation by dividing by the same multiplier. A 20% discount leaves 80% of the original price, so a final price of 80 must be divided by 0.80—not increased by 20%. This distinction prevents the most common reverse-percentage error.
Formula
Original after increase = Final ÷ (1 + r) • Original after decrease = Final ÷ (1 − r)How to use this reverse percentage calculator
- 1Enter the known final amount after the percentage was applied.
- 2Enter the percentage rate and choose increase or decrease.
- 3Read the recovered original value, multiplier, and forward check.
Reverse percentage examples for prices and growth
Each example keeps the base value visible so the calculation can be easily verified.
| Scenario | Substituted Formula | Result |
|---|---|---|
| 80 after a 20% discount | 80 ÷ (1 − 0.20) | Original = 100 |
| 120 after a 20% increase | 120 ÷ (1 + 0.20) | Original = 100 |
| 425 after a 15% decrease | 425 ÷ (1 − 0.15) | Original = 500 |
Common reverse percentage calculator Mistakes
Adding the percentage back
Increasing a discounted final price by the same rate does not reverse the discount because the base has changed.
Using the rate instead of the multiplier
For a 25% decrease, divide by 0.75, the proportion that remains—not by 0.25.
Allowing a 100% decrease
A 100% decrease produces zero from any original amount, so a unique original cannot be recovered.
Percentage Calculator Cluster
Choose another percentage calculation
Frequently Asked Questions
Convert the discount to a decimal, subtract it from 1, and divide the sale price by that remaining multiplier. A sale price of 75 after 25% off gives 75 ÷ 0.75 = 100.
The percentage is applied to a different base. After 20% off 100, the result is 80; adding 20% of 80 returns only 96.
Yes. It divides by 1 plus the decimal rate for an increase and by 1 minus the decimal rate for a decrease.
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