Percentage Calculator

Calculate percentages, percentage changes, and percentage differences.

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Guide

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.

Basic Percentage Formula:
Percentage = (Value ÷ Total Value) × 100

Core Percentage Calculations

  1. Finding the percentage of a value: Multiply the value by the percentage (as a decimal).

    25% of 80 = 0.25 × 80 = 20
  2. 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%
  3. 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

((Final Value - Initial Value) ÷ Initial Value) × 100

When a value increases from 50 to 75, the percentage increase is ((75-50) ÷ 50) × 100 = 50%

Percentage Decrease

((Initial Value - Final Value) ÷ Initial Value) × 100

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)

75% = 0.75

Decimal to Percentage

Multiply by 100 (or move decimal point two places right)

0.35 = 35%

Fraction to Percentage

Divide numerator by denominator and multiply by 100

3/4 = 0.75 = 75%
Concept

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.

Percentage Formula:
Percentage = (Value / Total) × 100
Steps

Calculation Methods

Here are the methods for calculating percentages:

  1. 1
    Percentage of a Value: Multiply the value by the percentage and divide by 100
  2. 2
    Percentage Change: Divide the difference by the original value and multiply by 100
  3. 3
    Percentage Difference: Divide the absolute difference by the average and multiply by 100

For example, to calculate 20% of 100:

Example Calculation:
20% of 100 = (20 × 100) ÷ 100 = 20
Examples

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

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