Percentage change compares a signed change with the magnitude of its original value. It distinguishes increase from decrease.
Use it to compare before-and-after prices, measurements, counts, or performance against their starting point.
The relationship
The defining equation
change % = (new − original)/|original| × 100
The numerator is the signed change; the absolute original magnitude supplies the reference scale.
See the structure
Measure the change against where you started
80+2010020 ÷ 80 = +25%
Worked example
Increase from 80 to 100
(100−80)/|80| × 100% = 25%
Interpret with care
What the result does—and does not—mean
A zero original value has no finite relative percentage change. Percentage change is directional and is not the symmetric percentage-difference measure.
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
percentage change = (new − original)/|original| × 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
Changing from 80 to 100 is a 25% increase.
percentage change = (new − original)/|original| × 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
A zero original value has no defined relative percentage change.
