A percentage is a fraction expressed as a portion of 100, denoted by the % symbol. It is used universally in discounts, interest rates, tax, tips, grades, and statistical analysis.
Common Percentage Formulas
- What is X% of Y? Answer = Y × (X/100). Example: 15% of 200 = 200 × 0.15 = 30
- X is what % of Y? Answer = (X/Y) × 100. Example: 45 is what % of 180? (45/180) × 100 = 25%
- Percentage Change: ((New − Old) / Old) × 100. Example: Price from $80 to $100: ((100-80)/80) × 100 = 25% increase
Why Percentages Matter
Percentages normalize different quantities to a common scale, making comparisons meaningful. Saying "sales grew by $50,000" is less informative than "sales grew by 12%" — the percentage gives context relative to the starting point.
Real-World Example
A store offers 30% off a $250 item. Discount: $250 × 0.30 = $75. Sale price: $250 − $75 = $175. If sales tax is 8.5%: $175 × 0.085 = $14.88. Total: $189.88.
Frequently Asked Questions
How do I calculate percentage increase or decrease?
Percentage change = ((New Value − Original Value) ÷ Original Value) × 100. A positive result is an increase; negative is a decrease. Always divide by the original (starting) value, not the new value.
What is the difference between percentage and percentile?
Percentage is a fraction of 100 (e.g., "you scored 85%"). Percentile indicates relative ranking (e.g., "you scored in the 90th percentile" means you scored higher than 90% of test takers). They measure different things.
Why do two successive 50% changes not return to the original?
A 50% increase on $100 gives $150. A 50% decrease on $150 gives $75 — not $100. This is because the second percentage is applied to the new (larger) number. Percentage increases and decreases are not symmetric.