Percentage calculator
Reverse Percentage Calculator
Reverse percentage calculations recover a starting value from a final value when the percentage increase or decrease is known.
Original value
100
Value before the percentage change.
Formula
Final Value / (1 − Discount / 100)Step-by-step calculation
- 1
Enter the value after the percentage change.
- 2
Enter the percentage change.
- 3
Divide by the applicable percentage factor to recover the original value.
Formula
After increase: Original = Final ÷ (1 + Rate ÷ 100) After decrease: Original = Final ÷ (1 − Rate ÷ 100)
How to calculate it
- Identify whether the final value resulted from an increase or a decrease.
- Convert the percentage rate into a decimal multiplier.
- Divide the final value by that multiplier to recover the original.
Recover a price after a 20% increase
Values: Final price = 120; increase = 20%.
Result: 120 ÷ 1.20 = 100 original price.
Frequently asked questions
Why not subtract 20% from the final value?
The increase was calculated from the original value, not the final value. Dividing by the increase multiplier reverses the operation correctly.
Can a 100% decrease be reversed?
No. A 100% decrease produces a final value of zero, and the original value cannot be recovered from zero using this formula.
Does reverse percentage work for increases and decreases?
Yes, but the multiplier is different: 1 plus the rate for an increase and 1 minus the rate for a decrease.