Reverse percentage works backward from a final value to the original value before an increase or decrease.
Use it when a displayed price, population, score, or amount already includes a known percentage change.
The relationship
The defining equation
original = final / (1 ± p/100)
Use plus after an increase and minus after a decrease; p is the stated change rate.
See the structure
Undo the multiplier, not the final amount
100+20120120 ÷ 1.20 = 100
Worked example
Undo a 20% increase
original = 120 ÷ 1.20 = 100
Interpret with care
What the result does—and does not—mean
Subtracting 20% from 120 does not undo a 20% increase because the two percentages use different reference values.
Quick guide
How to use this calculator
Enter the known values using ordinary signed decimals.
Choose an interpretation or relationship when the calculator provides one.
Read the exact result, decimal preview, and any domain explanation.
Calculation method
Use the stated percentage or ratio relationship
original = final/(1 ± percentage/100)
The calculator keeps finite-decimal inputs as exact reduced fractions and rejects a zero reference or denominator whenever the requested relative quantity would be undefined.
Worked example
Worked interpretation
A final value of 120 after a 20% increase came from 100.
original = final/(1 ± percentage/100)
Supported inputs
Precision and limits
Input precision
Each value may contain up to 30 digits and 15 decimal places. Scientific notation, fractions typed with a slash, and thousands separators are not accepted.
Exactness
Finite decimals are converted to reduced rational numbers. Detected repeating digits appear in parentheses, while previews that exceed the display limit end with an ellipsis; the exact fraction remains available.
Lists and ratios
List-based tools accept 2–12 entries separated by commas, colons, semicolons, or new lines. Ratio parts must satisfy the positivity rules shown by the calculator.
Calculator-specific rule
After a 100% decrease, a zero final value has no unique original; a nonzero final value has no solution.
