Ratio Calculator (simplify and solve proportions)

Ratios and proportions

A ratio compares two quantities — 3 : 4 means three of one thing for every four of another. A proportion says two ratios are equal, and that equality lets you find a missing value whenever you know the other three.

A : B = C : D  →  A × D = B × C

Cross-multiplication

Because the two ratios are equal, multiplying diagonally across the equals sign gives two products that must match. Rearranging that gives whichever value you're missing: D = B × C / A, or C = A × D / B, and so on. This is the single most useful trick in everyday maths — it powers recipe scaling, map distances, currency sums, and unit pricing.

Simplifying

A ratio in lowest terms divides both sides by their greatest common divisor, so 12 : 18 becomes 2 : 3. The value doesn't change; it's just easier to read and compare. The GCD calculator finds that divisor, and the same reduction is what puts afraction in lowest terms.

Worked example

A recipe for 4 people needs 3 cups of flour; how much for 9 people? Set it up as 3 : 4 = x : 9 — wait, keep the same order: flour to people is 3 : 4, so x : 9 must match, giving x = 3 × 9 / 4 = 6.75 cups. The order matters — always put the same kind of quantity in the same position on both sides, or the answer comes out inverted.

A ratio says nothing about scale

Simplifying is exact integer arithmetic. What a ratio cannot tell you is magnitude: 2:3 describes the same relationship whether the quantities are grams or tonnes, so the units have to be carried alongside and must match on both sides. Comparing a ratio in centimetres against one in inches produces a number that looks fine and means nothing — convert first, using the length converter if needed.