Calculation Breakdown
Reverse percentage calculation works backwards from the final value to recover the starting value.
Final value = Original × (1 + Rate ÷ 100)
Original = 120 ÷ (1 + 20 ÷ 100)
Original = 120 ÷ 1.2 = 100
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Reverse Percentage Calculator
Find the original value before a percentage increase or decrease.
Explore the reverse percentage formula with a clear, step-by-step solution.
01
Find the Original Value
Enter the final value and the percentage change applied to it.
YOUR RESULT
Original Value Result
120 is the final value after a 20% increase.
100The original value was 100.
Change amount: +20
✓VerifiedCalculation
Formula Used
The formula depends on whether the value increased or decreased.
After an increase
Original Value = Final Value ÷ (1 + Rate ÷ 100)
120 ÷ (1 + 20 ÷ 100) = 100
For a decrease, the rate must be less than 100% to recover a positive original value from a positive final value.
Step-by-Step Solution
Follow each step to see how the original value is calculated.
1
Convert the percentage into a multiplier1 + 20 ÷ 100 = 1.2
2
Divide the final value by the multiplier120 ÷ 1.2 = 100
3
Check by applying the increase100 × 1.2 = 120
LEARN THE CONCEPT
What Is a Reverse Percentage?
A reverse percentage calculation finds the starting value when you know the final value and the percentage increase or decrease. For example, if a price becomes 120 after a 20% increase, the original price was 100—not 96—because the 20% increase is calculated from the original amount.
This method is useful for finding a pre-discount price, an original salary before a raise, a starting cost before tax or markup, and the value before a percentage reduction. The key is to divide by the correct multiplier rather than simply adding or subtracting the percentage from the final value.
FORMULA EXPLAINED
How to Calculate Reverse Percentage
First convert the percentage rate into a multiplier. Divide the final value by that multiplier to recover the original value.
After an increase=
Original = Final ÷ (1 + Rate ÷ 100)
After a decrease=
Original = Final ÷ (1 − Rate ÷ 100)
Worked Example
Final value: 120 after a 20% increase
Multiplier = 1 + 20 ÷ 100 = 1.2
Original = 120 ÷ 1.2
= 100Reverse Percentage Examples
Reverse Percentage Formulas
Original before an increaseFinal ÷ (1 + Rate ÷ 100)
Original before a decreaseFinal ÷ (1 − Rate ÷ 100)
Final after an increaseOriginal × (1 + Rate ÷ 100)
Final after a decreaseOriginal × (1 − Rate ÷ 100)
A 20% increase and a 20% decrease are not reverse operations on the same final value. Always divide by the appropriate multiplier to find the starting amount.
Reverse Percentage Calculator FAQs
How do I find the original value after a percentage increase?
Divide the final value by 1 plus the percentage rate divided by 100. For example, 120 ÷ 1.2 = 100 after a 20% increase.
How do I find the original value before a discount?
Divide the discounted final value by 1 minus the discount rate divided by 100. For example, 80 ÷ 0.8 = 100 after a 20% discount.
Why can't I subtract 20% from 120 to reverse a 20% increase?
The increase was calculated from the original value, not the final value. To reverse it correctly, divide 120 by 1.2, which gives 100.
Can I reverse a 100% decrease?
No. A 100% decrease leaves a final value of zero, so the original value cannot be uniquely recovered by dividing by the remaining percentage multiplier of zero.