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.
Missing Value
--
Simplified Ratio (A : B)
--
Equivalent Ratio (C : D)
--
Ratios Are Equivalent?
--
Ratio as Fraction (A/B)
--
Ratio as Percentage (A/B)
--
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.
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.
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.
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.
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.
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.
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.
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.