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Ratio Calculator (Simplify & Solve Proportions)
A ratio compares the relative sizes of two or more quantities. In mathematics, architecture, cooking, and financial analysis, maintaining proportional equivalence ensures structural integrity, flavor balance, and accurate scale modeling. This calculator simplifies ratios to lowest terms and solves for unknown variables in proportional equations.
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How to Use This Tool Step-by-Step
- Choose mode: ‘Simplify Ratio’ (e.g. 24 : 36) or ‘Solve Proportion’ (A : B = C : D).
- Enter your numerical terms.
- Click Calculate to view simplified ratios, scale factors, and cross-multiplication steps.
📐 Mathematical Ratio Principles
• Simplification: Divide both terms by their Greatest Common Divisor (GCD): A ÷ GCD : B ÷ GCD • Proportion Equation: A / B = C / D • Cross-Multiplication: A × D = B × C => D = (B × C) ÷ A
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Proportion Solution Example
Solve 4 : 5 = 20 : X:
1. Cross-multiply: 4 × X = 5 × 20
2. 4X = 100
3. Divide by 4: X = 100 ÷ 4 = 25.
📊 Reference Benchmarks & Classification Data
| Original Ratio | Greatest Common Divisor (GCD) | Simplified Ratio | Decimal Ratio (1 : n) |
|---|---|---|---|
| 12 : 18 | 6 | 2 : 3 | 1 : 1.5 |
| 24 : 36 | 12 | 2 : 3 | 1 : 1.5 |
| 15 : 75 | 15 | 1 : 5 | 1 : 5.0 |
| 48 : 64 | 16 | 3 : 4 | 1 : 1.33 |
❓ Frequently Asked Questions (FAQ)
What is the difference between a ratio and a proportion?
A ratio compares two quantities (e.g., 3 boys to 2 girls). A proportion is a mathematical statement that two ratios are equal (e.g., 3/2 = 6/4).
How are ratios used in recipe scaling?
To scale a recipe designed for 4 people to serve 10 people, calculate the scale factor: 10 ÷ 4 = 2.5. Multiply every ingredient quantity by 2.5.