How to Calculate Percentages
A percentage is a way of expressing a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used everywhere — from shopping discounts and tax calculations to exam scores and financial reports.
The Basic Percentage Formula
To find X% of a number Y, use this formula:
Example: What is 15% of 300?
Result = (15 / 100) × 300 = 0.15 × 300 = 45
How to Find What Percentage One Number Is of Another
To find what percentage X is of Y:
Example: 45 is what percent of 300?
Percentage = (45 / 300) × 100 = 15%
How to Calculate Percentage Increase or Decrease
The percentage change formula measures how much a value has increased or decreased relative to its original value:
Example: A product's price increased from $80 to $100.
% Change = ((100 - 80) / 80) × 100 = (20 / 80) × 100 = 25% increase
Percentage Difference Between Two Values
Unlike percentage change, percentage difference treats both values equally — it doesn't matter which came first:
Example: Compare 80 and 100.
% Difference = (|80 - 100| / ((80 + 100) / 2)) × 100 = (20 / 90) × 100 = 22.22%
Common Percentage Conversions
Here are the most commonly used percentages and their fraction/decimal equivalents:
- 10% = 1/10 = 0.1
- 20% = 1/5 = 0.2
- 25% = 1/4 = 0.25
- 33.33% = 1/3 = 0.333...
- 50% = 1/2 = 0.5
- 75% = 3/4 = 0.75
Real-World Applications of Percentages
Percentages are essential in everyday life:
- Shopping: Calculate discounts — "30% off $59.99" = $41.99
- Finance: Interest rates, investment returns, inflation
- Taxes: Income tax brackets, sales tax, property tax
- Education: Exam scores, GPA calculations
- Health: BMI, body fat percentage, nutrition labels
- Business: Profit margins, growth rates, market share
Frequently Asked Questions
How do I calculate a percentage of a number?
To find X% of a number, multiply the number by X and divide by 100. For example, 25% of 200 = 200 × 25 / 100 = 50. You can also convert the percentage to a decimal first: 25% = 0.25, then 0.25 × 200 = 50.
How do I calculate percentage increase?
Percentage increase = ((New Value - Old Value) / Old Value) × 100. For example, if a price goes from $50 to $65, the increase is ((65-50)/50) × 100 = 30%.
What is the percentage difference formula?
Percentage difference = (|Value1 - Value2| / ((Value1 + Value2) / 2)) × 100. This calculates the relative difference between two values, treating them symmetrically.
How do I convert a fraction to a percentage?
Divide the numerator by the denominator, then multiply by 100. For example, 3/4 = 0.75 = 75%.
How do I calculate percentage off a price?
Multiply the original price by (1 - discount/100). For example, 20% off $80: $80 × (1 - 20/100) = $80 × 0.8 = $64. You save $16.