Understanding Percentages

A percentage is a number expressed as a fraction of 100. The word comes from the Latin "per centum," meaning "by the hundred." Percentages are used to express how large or small one quantity is relative to another quantity.

Common Percentage Calculations

Finding the Percentage of a Number

To find X% of Y, multiply Y by X/100. For example, to find 15% of 80:

15% of 80 = (15/100) × 80 = 0.15 × 80 = 12

Finding What Percentage X is of Y

To find what percentage X is of Y, divide X by Y and multiply by 100. For example, to find what percentage 12 is of 80:

12 is what % of 80? = (12/80) × 100 = 0.15 × 100 = 15%

Calculating Percentage Increase or Decrease

To find the percentage increase or decrease from X to Y:

Percentage change = ((Y - X) / X) × 100

For example, if a price increases from $80 to $100:

Percentage increase = ((100 - 80) / 80) × 100 = (20/80) × 100 = 25%

Practical Applications of Percentages

Finance: Interest rates, tax rates, discounts, and investment returns
Business: Profit margins, growth rates, and market share
Statistics: Expressing probabilities and proportions
Education: Grading systems and test scores
Science: Concentration solutions and experimental results

Tips for Working with Percentages

Remember that 100% of a number is the number itself
To convert a percentage to a decimal, divide by 100
To convert a decimal to a percentage, multiply by 100
A percentage increase of 100% means the value has doubled
A percentage decrease of 100% means the value has become zero

Percentage Calculator

Common Percentages

How to Calculate Percentage of a Number