Percentage Calculator
Calculate percentages, percentage changes, and percentage differences.
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Table of Contents
Comprehensive Percentage Calculator Guide
A percentage is a number or ratio expressed as a fraction of 100. The symbol "%" represents percentage. Percentages provide a standardized way to compare quantities, express changes, calculate portions, and make financial decisions.
Understanding Percentages
The word "percentage" comes from the Latin "per centum," meaning "by the hundred." When we say 25%, we're saying 25 out of 100, or 25/100 as a fraction. Percentages allow us to express fractions in a standardized form that's easier to compare and understand.
Core Percentage Calculations
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Finding the percentage of a value: Multiply the value by the percentage (as a decimal).
25% of 80 = 0.25 × 80 = 20 -
Finding what percentage one value is of another: Divide the part by the whole and multiply by 100.
15 is what percent of 60? (15 ÷ 60) × 100 = 25% -
Finding the original value when given a percentage: Divide the part by the percentage (as a decimal).
30 is 40% of what number? 30 ÷ 0.4 = 75
Percentage Change and Difference
Percentage change calculations are vital for analyzing increases and decreases in values over time.
Percentage Increase
When a value increases from 50 to 75, the percentage increase is ((75-50) ÷ 50) × 100 = 50%
Percentage Decrease
When a value decreases from 80 to 60, the percentage decrease is ((80-60) ÷ 80) × 100 = 25%
Practical Applications of Percentages
Finance
- Interest rates
- Discounts and taxes
- Investment returns
- Profit margins
Business
- Market share
- Growth rates
- Sales performance
- Profit/loss analysis
Daily Life
- Calculating tips
- Shopping discounts
- Academic grades
- Nutrition labels
Mental Math Shortcuts for Percentages
These mental math techniques can help you calculate percentages quickly:
- 10% of a number: Move the decimal point one place to the left (10% of 250 = 25)
- 1% of a number: Move the decimal point two places to the left (1% of 250 = 2.5)
- 5% of a number: Calculate 10% and divide by 2 (5% of 250 = 25 ÷ 2 = 12.5)
- 25% of a number: Divide by 4 (25% of 250 = 250 ÷ 4 = 62.5)
- 20% of a number: Divide by 5 (20% of 250 = 250 ÷ 5 = 50)
- 50% of a number: Divide by 2 (50% of 250 = 250 ÷ 2 = 125)
Converting Between Percentages, Decimals, and Fractions
Percentage to Decimal
Divide by 100 (or move decimal point two places left)
Decimal to Percentage
Multiply by 100 (or move decimal point two places right)
Fraction to Percentage
Divide numerator by denominator and multiply by 100
Percentage Concept
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign "%". Percentages are used to express how large or small one quantity is relative to another quantity.
Calculation Methods
Here are the methods for calculating percentages:
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1Percentage of a Value: Multiply the value by the percentage and divide by 100
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2Percentage Change: Divide the difference by the original value and multiply by 100
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3Percentage Difference: Divide the absolute difference by the average and multiply by 100
For example, to calculate 20% of 100:
Percentage - Practical Examples
Example 1 Discounts
Calculating discounts on products using percentages.
20% off $100 = $20 discount
Example 2 Tax Calculations
Calculating sales tax on purchases.
8% tax on $50 = $4 tax
Example 3 Grade Calculations
Calculating grades based on percentage scores.
85% of 100 points = 85 points