Ratio Calculator
Solve proportions (A:B = C:?), simplify ratios to lowest terms, scale recipes, and convert ratios to fractions, decimals, and percentages.
Solved Value (D)
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Simplified A:B —
Ratio as Decimal —
A as % of Total —
Extended More scenarios, charts & detailed breakdown ▾
D (missing value)
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Verification A/B = C/D —
Professional Full parameters & maximum detail ▾
Ratio Forms
Simplified A:B —
Simplified A:B:C —
A:B as Decimal —
A:B as Fraction —
Percentage Breakdown
A as % of (A+B) —
B as % of (A+B) —
Special Ratios
Golden Ratio Distance —
Aspect Ratio (W:H simplified) —
How to Use This Calculator
Enter values A, B, C and leave D as 0 to solve the proportion A:B = C:D. Or use the tabs to simplify a ratio, check the golden ratio, or scale a recipe.
Formula
Proportion: D = (C × B) / A • Simplify: divide both by GCD(A, B)
Example
2:3 = 4:? → D = (4×3)/2 = 6. Simplified ratio 12:18 = 2:3.
Frequently Asked Questions
- A proportion states that two ratios are equal: A:B = C:D. To solve for the unknown (D), use cross-multiplication: A × D = B × C, so D = (B × C) / A. Example: 2:3 = 8:D → D = (3 × 8) / 2 = 12. Verify: 2:3 = 8:12, both simplify to 2:3. Proportions are used everywhere — scaling recipes, converting units, finding similar triangle side lengths, and solving word problems involving rates and ratios.
- Divide both terms of the ratio by their Greatest Common Divisor (GCD). The result is the ratio in its simplest (lowest) form. Example: simplify 18:24. GCD(18, 24) = 6. Divide both by 6: 18÷6 = 3 and 24÷6 = 4, so 18:24 = 3:4. Another example: 100:250 → GCD = 50 → 2:5. For three-part ratios like 12:18:24, find the GCD of all three (GCD = 6) and divide each: 2:3:4. A simplified ratio cannot be reduced further (all terms have GCD = 1).
- The golden ratio φ (phi) ≈ 1.61803398... is a special mathematical constant defined by the proportion: a/b = (a+b)/a = φ. It satisfies φ² = φ + 1. A rectangle has "golden" proportions when its length-to-width ratio equals φ ≈ 1.618:1. The golden ratio appears in the Fibonacci sequence (the ratio of consecutive Fibonacci numbers converges to φ), and has been associated with art, architecture, and nature, including the proportions of the Parthenon and spiral patterns in shells.
- A ratio A:B is equivalent to the fraction A/B. For example, 3:4 = 3/4 = 0.75. However, there is a subtle difference in interpretation: a ratio 3:4 compares two separate quantities (3 parts of one thing to 4 parts of another), while a fraction 3/4 represents a part of a whole. In a mixture of 3 parts juice to 4 parts water, the ratio is 3:4 but the fraction of juice in the total is 3/7 (not 3/4). Always clarify whether a ratio describes parts-to-parts or part-to-whole.
- Identify the original serving count and the desired serving count, then compute the scale factor = desired servings / original servings. Multiply every ingredient quantity by this factor. Example: a recipe serves 4 but you want to serve 10. Scale factor = 10/4 = 2.5. If the original recipe needs 2 cups of flour, you need 2 × 2.5 = 5 cups. For reducing a recipe (fewer servings), the scale factor will be less than 1 — e.g., serving 2 from a recipe of 4 gives factor 0.5, so 2 cups becomes 1 cup.