How to Calculate Percentages
A percentage is a way of expressing a number as a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." Percentages are used everywhere — discounts, tax rates, test scores, statistics, and financial calculations.
Finding X% of a Number
To find X% of Y, convert the percentage to a decimal by dividing by 100, then multiply by the number:
Formula: Result = (X / 100) × Y
Example: 15% of 300 = (15/100) × 300 = 0.15 × 300 = 45
Finding What Percent X is of Y
To determine what percentage one number represents of another, divide the part by the whole and multiply by 100:
Formula: Percentage = (Part / Total) × 100
Example: What percent is 75 of 250? (75/250) × 100 = 30%
Calculating Percentage Change
Percentage change measures how much a value has increased or decreased relative to its original value:
Formula: % Change = ((New - Old) / |Old|) × 100
Example: A price went from $80 to $100. Change = ((100-80)/80) × 100 = 25% increase
Percentage Examples
- 20% of 500 = (20/100) × 500 = 100
- 45 is what % of 180? (45/180) × 100 = 25%
- Change from 200 to 250: ((250-200)/200) × 100 = 25% increase
- Change from 150 to 120: ((120-150)/150) × 100 = -20% (decrease)
When to Use Percentage Calculations
Percentages show up in almost every area of daily life and professional work:
- Shopping: Calculating discounts ("30% off") and sales tax
- Finance: Interest rates, investment returns, profit margins
- Education: Test scores, grading curves
- Statistics: Expressing proportions, survey results
- Cooking: Scaling recipes up or down by a percentage