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 Fraction Calculator.
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 Mixed Number Calculator 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 calculate Comparing Fractions Comparison Result as well.