This percentage calculator handles four common tasks: finding a percentage of a number, expressing one number as a percentage of another, measuring percentage change, and comparing two values by percentage difference.
How to use this calculator
Select the calculation first, then enter X and Y according to the labels. For change, X is the starting value and Y is the ending value. Percentage difference compares values symmetrically using their absolute average as denominator.
Formula & calculation method
X% of Y = XY/100; change = (Y−X)/|X|×100; difference = |Y−X|/average(|X|,|Y|)×100Each mode uses a different denominator. Finding X as a percentage of Y divides X by Y. Change uses the absolute starting value to preserve direction, while difference uses the average and is always nonnegative.
Worked example
20% of 150 is 30. A change from 150 to 180 is a 20% increase. In contrast, the percentage difference between 150 and 180 uses their average of 165, producing approximately 18.18%.
Why this is useful
One tool covers everyday shopping, finance, school, and data comparisons while keeping formulas visible. Mode labels reduce ambiguity about which value is the base and why change differs from percentage difference.
Limitations to keep in mind
Percentages can be misleading when the base is very small or zero. Change from zero is undefined, and percentage difference is undefined when both values are zero. Always check that the chosen mode matches the question.
Frequently asked questions
What is the difference between change and difference?
Change has a starting value and direction. Percentage difference is symmetric and compares two values with their average.
Can a percentage exceed 100%?
Yes. A value can be more than 100% of a base, and an increase can exceed 100% when the new value is more than double the original.
Why can't change start at zero?
Percentage change divides by the starting magnitude. Division by zero has no finite mathematical result.