Ratio Calculator

At its core, a ratio compares two or more quantities, showing how much bigger one is than the other. For a standard two-number proportion expressed as A : B = C : D, we use cross-multiplication to find any missing variable: C = (A * D) / B. To simplify a ratio, the calculator finds the Greatest Common Divisor (GCD) of all input numbers and divides each term by that shared factor. When scaling, terms are multiplied or divided uniformly by a given factor to enlarge or shrink the entire proportional set without altering the core relationship.

Imagine you are mixing a concentrated cleaning solution where the required ratio of water to cleaner is 4 parts water to 2 parts cleaner (4 : 2). However, you only have 10 units of water and need to find out how much cleaner to use to maintain the exact same concentration. First, we identify our variables: A = 4, B = 2, and our new value C = 10. Using the formula for a missing fourth value (D = (B * C) / A), we calculate: D = (2 * 10) / 4 = 20 / 4 = 5. Therefore, you need exactly 5 units of cleaner to maintain your 4 : 2 ratio.

When working with ratios, always ensure all measurements or quantities share the same unit before calculating; never mix inches with feet or grams with kilograms. Always reduce your final answer to its simplest form to make comparisons easier. Finally, remember that order matters immensely in ratios: the ratio of cats to dogs (3 : 2) is fundamentally different from the ratio of dogs to cats (2 : 3).