Ratio Calculator

Calculate ratios and proportions for various applications.

Simplify a Ratio

Frequently Asked Questions

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About This Calculator

Ratio Calculator

Calculate and simplify ratios instantly with our free online calculator. Find equivalent ratios, scale ratios, compare quantities, and solve proportion problems with detailed explanations.

What is a Ratio?

A ratio is a relationship between two or more numbers that shows their relative sizes. Ratios compare quantities and tell us how much of one thing there is compared to another.

Basic Definition

Ratio of A to B: A : B or A/B

Example: In a class of 15 boys and 10 girls, the ratio of boys to girls = 15 : 10 = 3 : 2

Why Ratios Matter

  • Comparing Quantities: Understanding relative sizes
  • Scaling Recipes: Adjusting ingredient proportions
  • Maps and Models: Representing real-world proportions
  • Financial Analysis: Comparing investments, debt ratios
  • Problem Solving: Foundation for proportion problems

Types of Ratios

Part-to-Part Ratio: Compares different parts of a whole (e.g., Boys : Girls = 12 : 8 = 3 : 2)

Part-to-Whole Ratio: Compares a part to the entire whole (e.g., Boys : Total = 12 : 20 = 3 : 5)

Continued Ratio: Ratio of three or more quantities (e.g., Flour : Sugar : Milk = 4 : 2 : 1)

Simplifying Ratios

Divide by the Greatest Common Factor (GCF). Example: 15 : 25 = 3 : 5 (divide by 5)

Ratio Applications

  • Maps and Scale Models: Map scale 1:100,000 means 1 cm on map = 1 km in reality
  • Recipes and Cooking: Scale ingredients proportionally
  • Financial Ratios: Debt-to-Income Ratio analysis
  • Mixtures and Solutions: Fertilizer mix 3:1 (water:fertilizer)
  • Photography: Image dimensions like 4:3 or 16:9

Special Ratios

Golden Ratio (φ): φ ≈ 1.618, found in art, architecture, and nature

Pi (π): Circumference : Diameter = π : 1 ≈ 22:7

Aspect Ratios: 16:9 (widescreen), 4:3 (traditional), 21:9 (ultrawide)

Tips and Common Mistakes

  • Always simplify to lowest terms
  • Maintain order: First:Second matters
  • Use cross multiplication for proportion problems
  • Keep consistent units throughout