Ratio Calculator

How it works

A ratio compares two quantities using the syntax "A : B" — for example, a recipe with 2 cups of flour to 1 cup of sugar has a 2:1 flour-to-sugar ratio. Ratios are scale-free; doubling both sides preserves the relationship. The standard simplified form divides both terms by their greatest common divisor (GCD).

The calculator does two things. First, it simplifies any ratio you enter by dividing through the GCD: 8:12 simplifies to 2:3, 100:25 to 4:1. Second, it solves proportions of the form A:B = C:D where you supply A, B, and C, and the calculator computes D = (B × C) / A. Cross-multiplication is the standard technique: "A times D equals B times C", then solve for D.

Ratios appear all over practical math. Map scales (1:50,000), aspect ratios (16:9), gear ratios in mechanical systems, financial ratios (debt-to-equity), and concentration ratios in chemistry all work the same way. Recipe scaling uses proportions to convert from a recipe that serves 4 to one that serves 6.

A few caveats. Ratios with three or more terms (like 2:3:5) require simplifying by the GCD of all terms; this calculator handles two-term ratios. Ratios involving units must use consistent units on both sides — converting them via a different calculator first. Negative or zero values can produce odd results; ratios are conventionally defined for positive quantities.

If you need to express a ratio as a percentage, divide A by (A + B): the ratio 2:3 means the first part is 2/(2+3) = 40% of the whole. To convert a ratio to a fraction, write A/B directly.