Ratio Calculator

Simplify ratios and solve proportions. Find the missing value in a:b = c:? or simplify any ratio to its lowest terms.

First number in the ratio A:B.

Second number in the ratio A:B.

Known value for proportion solving (A:B = C:?).

Leave 0 to solve for D. Enter a value to check if proportions are equal.

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Understanding Ratios

A ratio compares two or more quantities, showing their relative sizes. The ratio 3:4 means for every 3 units of the first quantity, there are 4 units of the second. Ratios can be written as 3:4, 3/4, or "3 to 4." They are used in recipes, maps, scale models, and financial analysis.

Simplifying Ratios

To simplify a ratio, divide both numbers by their greatest common factor (GCF). For example, 12:18 → divide both by 6 → 2:3. A simplified ratio uses the smallest whole numbers possible while maintaining the same relationship between the quantities.

Solving Proportions

A proportion states that two ratios are equal: A/B = C/D. To find a missing value, cross-multiply: A × D = B × C. If A:B = 3:4 and C = 6, then D = (B × C) / A = (4 × 6) / 3 = 8. This technique is fundamental in scaling, unit conversion, and similar triangles.

Ratios in Everyday Life

Recipes use ratios (2 cups flour : 1 cup sugar). Maps use scale ratios (1:50,000). Financial ratios (debt-to-income, price-to-earnings) guide investment decisions. Mixing solutions, converting units, and resizing images all rely on maintaining correct ratios.

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