Percentage Calculator

Percentage Calculator handles four distinct questions that are often confused: a percentage of a number, one number as a percentage of another, directional percentage change, and symmetric percentage difference.

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What it does

Select the operation that matches the wording of your problem, then enter the First value and Second value. The order matters for percentage-of and percentage-change calculations.

Percentage change uses the original value as its denominator. Percentage difference instead divides the absolute gap by the average of both values, so it is useful when neither value is a baseline.

How to use this tool

  1. Choose the calculation: Select percent of a value, what percent, percentage change, or percentage difference.
  2. Enter both values: Fill First value and Second value in the order described by the selected formula.
  3. Read and label the result: Keep the original units when the result is a value; use the percent sign when the result is a rate.

Input and output

Input

  • First value
  • Second value
  • Calculation mode

Output

  • Calculated percentage or value for the selected mode

How it works

Percentage of

X% of Y is (X ÷ 100) × Y.

Change versus difference

Change is (new−old) ÷ old × 100. Difference is |A−B| ÷ ((A+B)÷2) × 100.

Practical example

Scenario
A price rises from 80 to 100.
Action
Choose Percentage change.
Input
First value (old) = 80; Second value (new) = 100
Expected result
The increase is 25%, because the 20-point rise is divided by the original 80.

Limitations

  • Percentage change is undefined when the original value is zero.
  • Percentage difference is undefined when the average of the two values is zero.
  • A percentage alone does not show the absolute size or practical significance of a change.
  • Displayed results are rounded; retain source precision for formal calculations.

Frequently Asked Questions

What is the difference between percentage change and percentage difference?

Change is directional and compares with an original baseline. Difference is symmetric and treats both observations equally.

Can a percentage increase exceed 100%?

Yes. Moving from 40 to 100 is an increase of 150%.

Why can a decrease never exceed 100% in ordinary positive quantities?

A 100% decrease takes a positive starting value to zero; going lower would imply a negative value.

Which number goes first?

For change, enter the old value first and new value second. For “A is what percent of B,” enter A first and B second.