Percentage Calculator

Calculate X% of Y, proportions, percentage increases or decreases, and symmetric percentage differences with the calculation base shown.

Check the base and sign convention when comparing these results with reports that use a different definition.

Calculated value30

Calculation explanation

Result = X × Y ÷ 100

Signed values are supported. For X as a percentage of Y, a zero denominator is undefined, including 0 ÷ 0.

How to use Percentage Calculator

Choose the percentage question before entering numbers. A proportion uses a specified whole, a change uses the original value, and a symmetric difference compares both magnitudes without selecting a starting point.

Choose a percentage operation; the input labels change to show the required values.
Enter the two values, including negative values where the selected formula allows them.
Read the result and formula together. A zero denominator produces a validation message rather than a percentage.

Formulas and assumptions

X% of Y = X × Y / 100; proportion = X / Y × 100.
Increase = (new − original) / |original| × 100; decrease reverses the numerator.
Symmetric difference = |X − Y| / ((|X| + |Y|) / 2) × 100.

A zero whole or zero original value makes the corresponding division undefined. Two zero values also have undefined percentage difference.
For signed changes this calculator uses the magnitude of the original as the base; a negative increase indicates a fall. This convention must be stated when reporting negative-base changes.
Difference uses average magnitudes for signed inputs, ranges from 0% to 200%, and is not a directional change. Results display up to six decimal places.

Practical examples

Calculate a proportion

Input: 15% of 200
Result: Calculated value: 30

Multiply 200 by 0.15.

Measure a price rise

Input: Original 80, new 100
Result: Percentage increase: 25%

The increase of 20 is one quarter of the original 80.

Compare two readings

Input: Values 80 and 100
Result: Percentage difference: 22.222222%

The gap of 20 is divided by the average magnitude of 90.

Frequently asked questions

What is the difference between percentage change and percentage difference?

Percentage change (increase or decrease) has an explicit starting value and measures directional movement: ((New − Original) ÷ |Original|) × 100. Percentage difference compares two numbers without a directional start, dividing the absolute difference by the average of the two numbers' magnitudes.

Why does a 50% increase followed by a 50% decrease not return to the original number?

Because each calculation uses a different baseline amount. Starting with 100 and increasing by 50% gives 150. Decreasing 150 by 50% subtracts 75 (half of 150), leaving 75. Percentage operations are always relative to the value they are applied to.

How does this calculator handle division by zero or negative original numbers?

If the baseline whole or original value is zero, division by zero is mathematically undefined and the calculator displays an explicit error. When calculating percentage change from a negative base, the calculator divides by the absolute magnitude |original|, following standard mathematical conventions.