Percentage Calculator
Calculate percentages, percentage changes, increases, and decreases with step-by-step explanations
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What is a Percentage?
A percentage is a way of expressing 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 and financial data. The percent sign (%) is simply shorthand for "out of 100."
Basic Percentage Formulas
Finding X% of Y: Multiply Y by X and divide by 100, or multiply Y by X/100. For example, 20% of 150 = 150 × (20/100) = 30.
Finding what percentage X is of Y: Divide X by Y and multiply by 100. For example, 30 is what % of 150? (30/150) × 100 = 20%.
Percentage Change: ((New Value - Old Value) / Old Value) × 100. If a value increases from 50 to 75, the change is ((75-50)/50) × 100 = 50% increase.
Percentage Increase and Decrease
To increase a value by a percentage, multiply the original value by (1 + percentage/100). For example, to increase 200 by 15%, calculate 200 × 1.15 = 230.
To decrease a value by a percentage, multiply the original value by (1 - percentage/100). For example, to decrease 200 by 15%, calculate 200 × 0.85 = 170.
Common Percentage Shortcuts
Some percentages are easy to calculate mentally. 10% of any number is just that number divided by 10. 50% is half. 25% is a quarter. 1% is dividing by 100. You can combine these: to find 15%, find 10% and 5% (which is half of 10%) and add them together.
Real-World Applications
Percentages are essential in finance (interest rates, investment returns), retail (discounts, sales tax), academics (test scores, grade percentages), health (body fat percentage, nutrition labels), and statistics (survey results, probability). Understanding how to calculate and interpret percentages helps you make informed decisions in virtually every aspect of life.
Important Note About Percentage Changes
Percentage increases and decreases are not symmetrical. If a stock price drops 50% from $100 to $50, it needs to increase 100% (not 50%) to get back to $100. This is because the percentage is calculated based on different base values. Always pay attention to what the percentage is "of."