What is a percentage?
A percentage expresses part of a whole on a scale of 100. That makes it a simple way to compare proportions, rates, and changes without worrying about the original units.
For example, 35% means 35 out of every 100, which is also 0.35 as a decimal. The same idea appears in discounts, tax rates, marks, conversion rates, and price changes.
If 25 students out of 50 are male, the fraction is 25 / 50 = 0.5. Multiply by 100 and you get:
0.5 x 100 = 50
So 25 out of 50 is 50%.
Percentage formula
The main percentage relationship is built around three values: the percentage itself, the base value, and the resulting amount.
P x V1 = V2
P is the percentage, V1 is the starting value, and V2 is the output after applying that percentage. This calculator accepts normal percentage entries, so you can type 5 instead of 0.05.
Example: What percentage of 30 is 1.5?
P = 1.5 / 30 = 0.05 = 5%
The same formula can be rearranged to solve for the missing base value or the missing result.
Percentage difference formula
Percentage difference shows how far apart two values are when neither number is treated as the starting point. It is useful for direct comparisons between two measurements.
Percentage Difference = |V1 - V2| / ((V1 + V2) / 2) x 100
The formula uses the average of the two numbers as the reference, then compares the gap to that average.
Example: |10 - 6| / ((10 + 6) / 2) = 4 / 8 = 50%
Percentage change formula
Percentage change compares a movement against the original value. This is the version people usually mean when they talk about a number increasing or decreasing by a percentage.
To increase a value, convert the percentage to decimal form and add it to 1. To decrease a value, subtract it from 1. Then multiply the original number by that factor.
Example: 500 increased by 10% = 500 x 1.10 = 550
Example: 500 decreased by 10% = 500 x 0.90 = 450