Free Ratio Calculator
Use this calculator to simplify a ratio, scale it by a factor, and solve proportions in one place.
Simplify & Scale a Ratio
Enter two numbers for A:B. Decimals are supported.
Proportion Solver
Solve A:B = C:D. Leave exactly one field blank to solve for it.
What is a ratio?
A ratio compares two quantities and shows how much of one value there is relative to another. You’ll usually see it written as A:B, as a fraction A/B, or in words like “A to B.” Ratios are used everywhere: recipes, budgeting, map scales, probability, screen dimensions, and business analytics.
How to use this ratio calculator
1) Simplify a ratio
Enter values for A and B, then click Calculate. The tool reduces the ratio to lowest terms using the greatest common divisor. For example, 8:12 simplifies to 2:3.
2) Scale a ratio
If you also enter a scale factor, the calculator multiplies both sides by that factor. This is helpful for increasing or decreasing batches, budgets, and design dimensions while keeping proportions constant.
3) Solve a proportion
Use the proportion section when you know three values in A:B = C:D. Leave one field blank and the calculator will solve the missing term with cross multiplication.
Practical examples
Recipe scaling
If flour to sugar is 3:2 and you want a batch 4 times larger, the scaled ratio is 12:8. Simplify back to 3:2 if needed, but use 12 and 8 as actual quantity units.
Personal finance
Suppose you use a 50:30:20 budgeting rule (needs:wants:savings). Ratios make it easy to split income consistently. If monthly income changes, you can scale the same ratio quickly.
Image and screen dimensions
Common aspect ratios like 16:9 or 4:3 are just ratios. If one side is known, a proportion finds the other side to avoid distortion.
Manual method (without a calculator)
- Write the ratio as A:B.
- Find the greatest common divisor (GCD) of A and B.
- Divide both numbers by the GCD.
- For proportions, use cross multiplication: if A/B = C/D, then A×D = B×C.
Common mistakes to avoid
- Mixing units: Compare like with like (minutes to minutes, dollars to dollars).
- Forgetting order: 2:5 is not the same as 5:2.
- Rounding too early: Keep precision until the final step.
- Using two unknowns in a proportion: You need exactly one missing value to solve directly.
Ratio calculator FAQ
Can I use decimals?
Yes. This calculator supports decimal inputs and still simplifies the ratio correctly.
What if one value is zero?
Ratios with zero can be expressed (such as 0:5), but proportions that require division by zero are undefined and will return an error message.
What’s the difference between ratio and fraction?
A fraction is typically part-to-whole. A ratio can be part-to-part or part-to-whole, depending on context.
Final thoughts
A good ratio calculator saves time, reduces arithmetic mistakes, and makes proportional reasoning easier in daily life. Whether you’re scaling a recipe, working on budget allocations, or solving geometry problems, clear ratios help you make better decisions faster.