Ratio Calculator

Enter values for A, B, C, or D in the Ratio Calculator to solve proportions of the form A : B = C : D. Provide any three values and the calculator finds the missing fourth, simplifies the ratio to its lowest terms, and checks whether two ratios are equivalent. Works with whole numbers and decimals. Also try the Fraction Calculator.

First part of the left-side ratio

Second part of the left-side ratio

First part of the right-side ratio (leave blank to solve for C)

Second part of the right-side ratio (leave blank to solve for D)

Results

Missing Value

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Simplified Ratio (A : B)

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Equivalent Ratio (C : D)

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Ratios Are Equivalent?

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Ratio as Fraction (A/B)

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Ratio as Percentage (A/B)

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Results Table

Frequently Asked Questions

What is a ratio?

A ratio is a quantitative relationship between two numbers showing how many times one value contains or is contained within the other. Ratios can be expressed using a colon (3:4), as a fraction (3/4), or in words ('3 to 4'). They are used in everyday contexts like recipes, maps, and financial analysis. See also our calculate Result (Mixed Number), Result (Fraction) & Result (Decimal) — Mixed Number.

How does the Ratio Calculator solve for a missing value?

Given three of the four values in A : B = C : D, the calculator uses cross-multiplication to find the fourth. For example, if A, B, and C are known, it solves D = C × (B / A). This is the fundamental property of proportions.

How do I simplify a ratio to its lowest terms?

To simplify a ratio, divide both parts by their Greatest Common Divisor (GCD). For example, 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4. The calculator does this automatically for both the A:B and C:D sides.

How do I check if two ratios are equivalent?

Two ratios A:B and C:D are equivalent if A × D = B × C (cross-multiplication). For instance, 3:4 and 9:12 are equivalent because 3 × 12 = 36 and 4 × 9 = 36. The calculator compares this for you and reports yes or no. You might also find our calculate Decimal to Fraction Simplified Fraction useful.

What is the golden ratio?

The golden ratio (approximately 1:1.618, often denoted φ) is a special irrational number that appears frequently in art, architecture, and nature. A ratio A:B equals the golden ratio when (A+B)/A = A/B ≈ 1.618. It is considered aesthetically pleasing and appears in the proportions of the Parthenon, Leonardo da Vinci's works, and spiral shell growth.

What are three ways to express a ratio?

A ratio can be written using a colon (e.g., 3:5), as a fraction (3/5), or in plain language ('3 to 5'). It can also be converted to a decimal (0.6) or a percentage (60%) to make comparisons easier.

Can ratios include decimals or fractions?

Yes. While ratios are most intuitive as whole numbers, they can include decimals (e.g., 1.5:2.5). The calculator accepts decimal inputs and will still simplify and solve correctly. Scientific notation is also valid for very large or very small values.

What is the ratio of 3 to 5?

The ratio of 3 to 5 is written as 3:5 or 3/5. As a decimal it equals 0.6, and as a percentage it is 60%. It means for every 3 parts of one quantity there are 5 parts of another. It is already in its simplest form since the GCD of 3 and 5 is 1. Check out our Equivalent Fractions Calculator as well.