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
Mental Math Shortcuts
- 10%: Move the decimal one place left. 10% of $85 = $8.50
- 5%: Find 10%, then halve it. 5% of $85 = $4.25
- 20%: Find 10%, then double it. 20% of $85 = $17.00
- 1%: Move the decimal two places left. 1% of $85 = $0.85
- Any %: Combine the above. 15% = 10% + 5%. 7% = 5% + 1% + 1%
Handy trick: X% of Y equals Y% of X. So 8% of 50 = 50% of 8 = 4. Use whichever direction is easier to compute.
Percent vs Percentage Points
These terms are often confused but mean different things:
- Percentage points: The absolute difference between two percentages. Going from 5% to 7% is a 2 percentage point increase
- Percent change: The relative change. Going from 5% to 7% is a 40% increase (2/5 × 100)
This distinction matters in news, finance, and statistics. "Unemployment rose 2 percentage points" (5% → 7%) is very different from "unemployment rose 2 percent" (5% → 5.1%).