Ratio Calculator
Simplify ratios, compare ratios, scale values, and solve ratio problems with step-by-step solutions
Multiply each part of the ratio by this factor
Quick Examples
Quick Examples
Simplified Ratio
:: →
GCD
Fraction
Decimal
Percentage
%
Calculation Steps
Scaled Ratio (×)
:: × =
Scale factor:
How We Compared
Common Ratios Reference
| Ratio | Fraction | Decimal | Common Use |
|---|---|---|---|
| 1:1 | 1/1 | 1.0 | Equal parts |
| 1:2 | 1/2 | 0.5 | Half |
| 2:3 | 2/3 | 0.667 | Two-thirds |
| 3:4 | 3/4 | 0.75 | Three-quarters |
| 16:9 | 16/9 | 1.778 | Widescreen displays |
| 4:3 | 4/3 | 1.333 | Standard TV/Monitor |
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About Ratio Calculator
What is a Ratio Calculator?
A ratio calculator is a mathematical tool that helps you work with ratios - expressions that compare two or more quantities. Ratios are fundamental in mathematics and appear everywhere from cooking recipes to financial analysis.
How to Use This Calculator
Mode 1: Simplify Ratios
Enter any ratio (like 12:16) and get the simplified form (3:4).
Mode 2: Scale Ratios
Scale a ratio up or down by a factor. For example, scale 1:2 by 3 to get 3:6.
Mode 3: Compare Ratios
Check if two ratios are equivalent and see their relationship.
Understanding Ratios
What is a Ratio?
A ratio is a way to compare two or more quantities. It can be written as:
- a:b (colon notation)
- a/b (fraction notation)
- "a to b" (word notation)
Key Concepts
| Concept | Description | Example |
|---|---|---|
| Antecedent | First number in ratio | In 3:4, 3 is antecedent |
| Consequent | Second number in ratio | In 3:4, 4 is consequent |
| Equivalent Ratios | Ratios with same relationship | 2:3 = 4:6 = 6:9 |
| Simplest Form | Ratio with no common factors | 12:16 → 3:4 |
How to Simplify Ratios
- Find the Greatest Common Divisor (GCD) of all numbers
- Divide each number by the GCD
- The result is the simplified ratio
Example: Simplify 24:36
- GCD(24, 36) = 12
- 24 ÷ 12 = 2
- 36 ÷ 12 = 3
- Simplified: 2:3
Common Applications
Cooking & Recipes
- Scaling recipes up or down
- Mixing ingredients in proper proportions
Finance & Business
- Profit margins and ratios
- Debt-to-equity ratios
- Price-to-earnings ratios
Science & Engineering
- Gear ratios
- Scale models
- Chemical solutions
Everyday Life
- Map scales
- Mixing paint colors
- Sharing items fairly
Frequently Asked Questions
How do I simplify a ratio?
Divide all numbers in the ratio by their GCD (Greatest Common Divisor). For example, 15:25 simplified is 3:5.
What's the difference between a ratio and a fraction?
A ratio compares multiple quantities (like 3:4), while a fraction represents a part of a whole (like 3/4). They can often be converted between each other.
Can ratios have more than two numbers?
Yes! Ratios can compare multiple quantities. For example, a recipe might call for ingredients in a 1:2:3 ratio.
Tip: When working with ratios in real-world applications, always ensure your units match before comparing quantities.