How to Calculate Percentages
A percentage is a fraction of 100, denoted by the symbol %. It expresses a number as a proportion of a whole. Understanding percentages is fundamental for everyday math, finance, shopping discounts, grade calculations, and statistical analysis.
Formula: What is X% of Y?
Result = (X ÷ 100) × Y
Example: What is 20% of 150? → (20 ÷ 100) × 150 = 30
Formula: X is What % of Y?
Percentage = (X ÷ Y) × 100
Example: 45 is what % of 180? → (45 ÷ 180) × 100 = 25%
Formula: Percentage Change
Change % = ((New − Old) ÷ Old) × 100
A positive result means an increase; a negative result means a decrease.
Example: Price rose from $80 to $100 → ((100 − 80) ÷ 80) × 100 = +25%
Common Percentage Examples
| Percentage | Fraction | Decimal | Example (of 200) |
|---|---|---|---|
| 10% | 1/10 | 0.10 | 20 |
| 25% | 1/4 | 0.25 | 50 |
| 33.3% | 1/3 | 0.333 | 66.6 |
| 50% | 1/2 | 0.50 | 100 |
| 75% | 3/4 | 0.75 | 150 |
| 100% | 1 | 1.00 | 200 |