Ratio Calculator

Ratios describe how two or more quantities relate to one another, and being able to reduce, scale, and solve them is a practical skill across finance, cooking, mapmaking, and statistics. The tool here handles two jobs at once: it reduces a ratio A:B to its simplest form, and it finds the term D that makes C:D equivalent to A:B, which is how you scale a ratio up or down.

Behind the scenes, the math relies on a few well-established rules. To reduce a ratio, the calculator finds the greatest common divisor (GCD) of the terms and divides each one by it, so the relationship is preserved while the numbers shrink. Scaling works by multiplying or dividing every term by the same factor. The calculator finds the missing term by cross-multiplication: when A/B = C/D, the products A × D and B × C are equal, so D = (C × B) / A. Simplification is meant for whole numbers; with decimals, multiply both terms by 10 or 100 first (1.5:2.5 becomes 15:25, which simplifies to 3:5).

Unit consistency matters more than it first appears. Mixing measurements, such as comparing inches against feet without converting, quietly corrupts the result even when the arithmetic looks clean. Reduction trips people up too: dividing only one side, or stopping before you reach the true greatest common divisor, leaves the ratio half-simplified. Treat a ratio as a relationship rather than a fixed count, since scaling changes both parts together and never just one.