Smart Unit ConvertersSmart Unit Converters

Ratio Calculator

Simplify ratios and solve proportions with a missing value.

Enter three values and leave one blank to solve for the missing number. Or enter A and B to simplify the ratio.

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?What is the Ratio Calculator?

A ratio calculator simplifies ratios to their lowest terms (for example, 12:18 becomes 2:3) and solves proportions where one value is unknown (for example, 3:4 = x:12 gives x = 9). Ratios compare two quantities of the same kind — ingredients in a recipe, sides of a rectangle, parts of a mixture, or cost per unit — and are fundamental in cooking, map reading, finance, chemistry, construction, and design. Proportions extend ratios to equality between two ratios, a tool used for scaling drawings, converting recipes, and solving many everyday 'same rate' problems.

The Formula

Simplify: divide both parts by GCD(a, b). Solve a:b = c:d via cross-multiplication: a × d = b × c, then isolate the unknown.

Dividing both parts of a ratio by their greatest common divisor (GCD) reduces it to its simplest form without changing the underlying relationship — the simplified ratio describes the same proportion, just using smaller numbers. Cross-multiplication works because equal ratios have equal cross-products — it turns the proportion into a linear equation, which is easy to solve for any single unknown term.

Practical Examples

1

12:18 simplifies to 2:3 (GCD = 6) — useful when presenting mixing ratios or recipe proportions cleanly.

2

Recipe scaling: if 2 cups of flour are used per egg and you have 3 eggs, solving 2:1 = x:3 gives x = 6 cups.

3

Map scale 1:50,000 means 1 cm on the map equals 50,000 cm (500 m) in reality — the basis of all topographic navigation.

4

Dilution 1:10 usually means 1 part concentrate per 10 total parts (or sometimes 1 part concentrate plus 10 parts solvent — always confirm notation).

5

Mortar mix 1:4 for standard bricklaying means 1 part cement to 4 parts sand, the most common proportion in residential construction.

6

Paint tinting: achieving a specific color may require mixing 3 parts base with 1 part tint — a 3:1 ratio for consistent results.

Frequently Asked Questions

Divide both parts of the ratio by their greatest common divisor (GCD). For example, 12:18 has GCD 6, so dividing both gives 2:3 — the simplest equivalent form. This calculator does the GCD computation automatically.