Percentage Calculator
All percentage calculations in one place - find percentages, calculate changes, and more.
What is X% of Y?
X is what % of Y?
Percentage Change
Increase/Decrease by %
Understanding Percentages
What Are Percentages?
A percentage is a way to express a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Percentages are used everywhere in daily life - from calculating discounts and taxes to understanding statistics, growth rates, and financial returns. The symbol % represents "per hundred," so 25% means 25 out of 100, or 25/100, or 0.25 as a decimal.
Common Percentage Calculations
Finding a Percentage of a Number
Formula: (Percentage ÷ 100) × Number = Result
Example: What is 15% of 200? (15 ÷ 100) × 200 = 0.15 × 200 = 30. This is useful for calculating tips, discounts, and portions of totals.
Finding What Percent One Number Is of Another
Formula: (Part ÷ Whole) × 100 = Percentage
Example: 45 is what percent of 180? (45 ÷ 180) × 100 = 25%. This helps you understand proportions and completion rates.
Calculating Percentage Change
Formula: ((New - Old) ÷ Old) × 100 = Percentage Change
Example: Price increased from $50 to $65. ((65 - 50) ÷ 50) × 100 = 30% increase. Essential for tracking growth, inflation, and investment returns.
Increasing/Decreasing by a Percentage
Increase: Number × (1 + Percentage/100) | Decrease: Number × (1 - Percentage/100)
Example: Increase $80 by 25%: $80 × 1.25 = $100. Decrease $80 by 25%: $80 × 0.75 = $60. Used for taxes, discounts, and growth calculations.
Real-World Applications
- Shopping & Discounts: Calculate sale prices, compare deals, and understand savings (e.g., 30% off $100 = $70 final price).
- Finance & Investing: Track investment returns, understand interest rates, and calculate loan costs.
- Tipping & Gratuity: Quickly calculate appropriate tips at restaurants (15-20% is standard in many places).
- Taxes: Determine sales tax amounts and total costs (e.g., 8% tax on $50 = $4, total $54).
- Statistics & Data: Understand survey results, success rates, and proportions in reports.
- School & Grades: Calculate test scores, grade point averages, and academic progress.
- Business Metrics: Measure growth rates, profit margins, and market share changes.
- Health & Fitness: Track weight loss/gain percentages and body composition changes.
Common Percentage Mistakes to Avoid
- Confusing Percentage vs Percentage Points: A change from 10% to 15% is a 5 percentage point increase, but a 50% relative increase.
- Not Using the Correct Base: When calculating percentage change, always use the original (old) value as the denominator.
- Forgetting to Convert: Remember that 25% = 0.25 as a decimal. Multiply by 0.25, not 25.
- Double Discounting Errors: A 20% discount followed by 10% off is not 30% total - it's 28% (successive discounts multiply).
- Reversibility Error: If a stock drops 50% and then rises 50%, you don't break even - you're still down 25%.
Quick Mental Math Tips
- 10%: Move decimal point one place left (10% of 230 = 23)
- 5%: Find 10% and divide by 2 (5% of 230 = 23 ÷ 2 = 11.5)
- 25%: Divide by 4 (25% of 80 = 80 ÷ 4 = 20)
- 50%: Divide by 2 (50% of 160 = 80)
- 20%: Find 10% and multiply by 2 (20% of 75 = 7.5 × 2 = 15)
- 15%: Find 10%, find 5%, and add them (15% of 40 = 4 + 2 = 6)
Percentage Formulas
X% of Y
= Y × (X ÷ 100)
X is what % of Y
= (X ÷ Y) × 100
% Change
= ((New - Old) ÷ Old) × 100
Increase by X%
= Value × (1 + X÷100)