Ratio Calculator

A ratio compares two quantities, showing their relative sizes. Written as a:b (read "a to b"), it tells you how many times one value contains or is contained within the other. The ratio 2:3 means for every 2 units of the first quantity, there are 3 units of the second. Ratios appear in recipes (flour to sugar), maps (scale distances), financial analysis (debt to equity), and mixing paint colors.

Simplifying a ratio means dividing both parts by their greatest common factor (GCF) until no common factor remains. The ratio 12:18 simplifies to 2:3 because GCF(12, 18) = 6, and 12÷6 = 2, 18÷6 = 3. A ratio is in simplest form when the GCF of its parts is 1. Unlike fractions, ratios can compare unlike quantities (3 dogs to 2 cats) and can include zero in some contexts, though the second part is typically nonzero in this calculator.

Equivalent ratios represent the same relationship: 1:2, 2:4, 50:100, and 3:6 all express the same proportion. Multiplying or dividing both parts by the same number produces an equivalent ratio, just as with fractions. This property is the basis for scaling — if a recipe ratio of flour to sugar is 3:1, tripling the recipe gives 9:3, which simplifies back to 3:1.

Ratio problems often ask you to find a missing value. If 2:3 = 8:x, then x = (3 × 8) ÷ 2 = 12. The logic: since 2 was multiplied by 4 to get 8, multiply 3 by the same factor to get 12. Cross-multiplication formalizes this: if a/b = c/d, then ad = bc. Similarly, if 3:4 = x:16, then x = (3 × 16) ÷ 4 = 12. These proportional reasoning skills are foundational for algebra, chemistry stoichiometry, and unit rate problems.

Ratios differ from fractions in notation and interpretation. The ratio 2:3 describes a relationship between two separate quantities, while the fraction 2/3 describes one quantity as part of a whole. In a class of 5 students with a boy-to-girl ratio of 2:3, there are 2 boys and 3 girls — not 2/5 boys in the fractional sense, though that happens to equal 40%. Use this calculator to simplify ratios and solve for unknown values in proportional equations quickly and accurately.