What is a reverse percentage calculation?
A reverse percentage calculation works backward from a final value and a known percentage change to recover the original value. It is useful for finding pre-discount prices, pre-tax amounts, and values before a reported increase or decrease.
How to find the original value after a percentage increase
Convert the percentage to a decimal, add it to 1, and divide the final value by that factor. If 120 is the value after a 20% increase, divide 120 by 1.20 to get an original value of 100.
How to find the original value after a percentage decrease
Convert the percentage to a decimal, subtract it from 1, and divide the final value by the remaining factor. If 80 is the value after a 20% decrease, divide 80 by 0.80 to get 100.
Reverse percentage formulas
Worked examples
| Final value | Change | Original value |
|---|---|---|
| 120 | After 20% increase | 100 |
| 80 | After 20% decrease | 100 |
| 72 | After 20% decrease | 90 |
| 115 | After 15% increase | 100 |
Reverse percentage vs percentage change
Reverse percentage starts with a final value and known rate to find the unknown original. Percentage change starts with both the original and new values to find the rate. Use the calculation that matches the unknown in your problem.
Frequently asked questions
How do I find the original value before a percentage increase?
Divide the final value by 1 plus the percentage written as a decimal. For a 20% increase, divide by 1.20.
How do I reverse a percentage decrease?
Divide the final value by 1 minus the percentage written as a decimal. For a 20% decrease, divide by 0.80.
How do I find the price before a discount?
Treat the discounted price as the final value and choose After decrease. Enter the discount percentage to calculate the original price.
How do I find the price before VAT or tax was added?
Treat the tax-inclusive price as the final value and choose After increase. Enter the tax rate to calculate the pre-tax value.
Can I reverse a 100% decrease?
No. A 100% decrease always produces zero, regardless of the starting value, so there is no unique original value to recover.
What is the difference between reverse percentage and percentage change?
Reverse percentage finds an unknown original value from a known final value and rate. Percentage change finds the rate of change between two known values.