Ratio Calculator
Solve proportions, simplify ratios to lowest terms, and scale ratios by any factor.
Examples
| Input | Result |
|---|---|
| Solve: 3 : 5 = 9 : ? | 15 |
| Simplify: 12 : 8 | 3 : 2 |
| Scale 3 : 4 by factor 5 | 15 : 20 |
About this tool
This ratio and proportion calculator supports three operations: solving for an unknown value in a proportion, simplifying a ratio to its lowest terms, and scaling a ratio by a given factor. Each mode lives on its own tab so you can jump between them without losing your inputs.
Solving proportions uses cross-multiplication. Simplification divides both parts of the ratio by their greatest common divisor using the Euclidean algorithm. Scaling just multiplies both parts by the factor you provide. These are common operations in cooking, construction, and map reading where ratios describe how quantities relate to each other.
Frequently asked questions
How do you solve a proportion like A:B = C:X?
Cross-multiply and divide. If A:B = C:X, then X = (B * C) / A. For example, 3:5 = 9:X gives X = (5 * 9) / 3 = 15.
What does it mean to simplify a ratio?
Divide both sides of the ratio by their greatest common divisor (GCD). The ratio 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4.
When would I need to scale a ratio?
Scaling is useful for recipes, mixing solutions, or resizing designs. If a recipe calls for a 2:3 flour-to-sugar ratio and you want to multiply everything by 4, the scaled ratio is 8:12.