How to Calculate Percentages
A percentage represents a fraction of 100. The word comes from the Latin per centum, meaning "by the hundred." Percentages are ubiquitous in daily life — from sales tax and discounts to investment returns and grade scores. Our calculator handles the three most common percentage problems, each with a different formula.
Mode 1: What Is X% of Y?
This is the most common percentage calculation. To find X percent of Y, convert the percentage to a decimal by dividing by 100, then multiply by the number: Result = (X ÷ 100) × Y. For example, 15% of 200 = (15 ÷ 100) × 200 = 0.15 × 200 = 30. You use this when calculating tips, discounts, sales tax, or investment returns on a known principal.
- Sales discounts: A $80 jacket at 25% off → 25% of 80 = $20 off → you pay $60.
- Tax calculations: 8.5% sales tax on a $150 purchase → 8.5% of 150 = $12.75 in tax.
- Investment gains: A 12% annual return on $10,000 → 12% of 10,000 = $1,200 earned.
Mode 2: X Is What Percent of Y?
This finds the percentage that one number represents of another: Result = (X ÷ Y) × 100. Use this to express a part as a proportion of a whole. For example, 30 is what percent of 200? (30 ÷ 200) × 100 = 15%. Common uses include calculating exam scores (you got 42 out of 50 — what percentage?), market share, or portfolio allocation percentages.
- Test scores: 42 correct out of 50 → (42 ÷ 50) × 100 = 84%
- Budget analysis: Spent $1,200 on rent out of $4,000 income → (1,200 ÷ 4,000) × 100 = 30% of income
- Sales performance: Closed 18 of 60 leads → (18 ÷ 60) × 100 = 30% conversion rate
Mode 3: Percentage Change from X to Y
Percentage change measures how much a value has increased or decreased relative to its starting point: Result = ((Y − X) ÷ |X|) × 100. A positive result is an increase; a negative result is a decrease. For example, a stock price moving from $80 to $100 represents a (100 − 80) ÷ 80 × 100 = 25% increase. If it dropped from $100 to $80, that's (80 − 100) ÷ 100 × 100 = −20% — note that a 25% gain and a 20% loss are not symmetric.
- Stock returns: Price moved from $45 to $63 → 40% gain
- Salary changes: Salary went from $65,000 to $72,000 → 10.8% raise
- Inflation tracking: Price of goods rose from $2.50 to $2.85 → 14% inflation
- Year-over-year growth: Revenue grew from $1.2M to $1.5M → 25% growth
Common Percentage Mistakes to Avoid
- Percentage gain vs. percentage of original: If something rises 50% then falls 50%, you don't break even — you're down 25%. Gains and losses are asymmetric.
- Percentage points vs. percentages: If an interest rate rises from 2% to 3%, it rose by 1 percentage point but by 50% (relative change). These mean very different things.
- Base confusion: "20% off the sale price" vs. "20% off the original price" give different final amounts. Always clarify what the percentage applies to.
- Rounding errors: Calculating tax or commission on rounded intermediate figures can accumulate errors. Our calculator uses full precision before rounding the display.
Quick Mental Math Shortcuts
You don't always need a calculator for percentages. A few shortcuts: 10% of any number is just moving the decimal point one place left (10% of 340 = 34). 5% is half of 10%. 1% is moving the decimal two places left. 15% tip? Take 10% ($34) and add half of that ($17) → $51. 25% is simply dividing by 4. These mental math tricks let you estimate quickly when precision isn't required.