Ratio Calculator

Calculate, simplify, and compare ratios with our easy-to-use calculator. Solve proportion problems and find equivalent ratios instantly.

Value A Enter the first value in the ratio

Value B Enter the second value in the ratio

Value C (Optional) Enter a third value for three-part ratios

Output Format

Calculation Type

Scale Factor Enter a factor to scale the ratio (leave as 1 for original)

Simplify Ratio to Lowest Terms

Quick Examples:

How to Use This Calculator

Enter the values for your ratio in the input fields
Select the calculation type (simplify, find equivalent ratios, compare, or solve proportions)
Choose your preferred output format
Set a scale factor if you want to enlarge or reduce the ratio
Click Calculate to see the results

Formula Used


            Ratio Simplification: A:B = (A÷GCD):(B÷GCD)

            Equivalent Ratio: (A×k):(B×k) where k is the scale factor

            Proportion: A/B = C/D, so D = (B×C)/A

            Ratio Comparison: A:B > C:D if A×D > B×C

Where:

A, B, C, D = Values in the ratios
GCD = Greatest Common Divisor
k = Scale factor

Example Calculation

Real-World Scenario:

A recipe calls for 3 cups of flour to 2 cups of sugar. You want to make half the recipe. What's the new ratio of flour to sugar?

Given:

Original ratio = 3:2 (flour to sugar)
Scale factor = 0.5 (half the recipe)
Calculation type = Equivalent Ratio

Calculation:

New flour amount = 3 × 0.5 = 1.5 cups

New sugar amount = 2 × 0.5 = 1 cup

Result: The new ratio is 1.5:1, which simplifies to 3:2 (same ratio, smaller quantities)

Why This Calculation Matters

Practical Applications

Recipe scaling and ingredient proportions
Map scales and distance calculations
Financial ratios and investment analysis

Key Benefits

Maintains proportional relationships
Helps with scaling recipes and formulas
Essential for engineering and design work

Common Mistakes & Tips

A common mistake is leaving ratios unsimplified. For example, expressing a ratio as 8:12 instead of simplifying to 2:3. Always divide both terms by their greatest common divisor to get the simplest form of a ratio.

When solving proportions like A:B = C:D, a common error is cross-multiplying incorrectly. Remember that A/B = C/D, so A×D = B×C. For example, if 2:3 = 4:x, then 2×x = 3×4, so x = 12/2 = 6.

While ratios can be expressed as fractions, they represent different concepts. A ratio compares two quantities, while a fraction represents a part of a whole. For example, the ratio 2:3 means for every 2 units of the first quantity, there are 3 units of the second, not that the first quantity is 2/3 of the second.

Frequently Asked Questions

To find equivalent ratios, multiply or divide both terms of the ratio by the same number. For example, if you have the ratio 2:3, multiplying both terms by 2 gives you the equivalent ratio 4:6. Dividing both terms by 2 would give you 1:1.5. All these ratios represent the same proportional relationship.

To compare two ratios A:B and C:D, cross-multiply and compare the products. If A×D > B×C, then A:B > C:D. For example, to compare 2:3 and 3:4, calculate 2×4 = 8 and 3×3 = 9. Since 8 < 9, the ratio 2:3 is less than 3:4.

To solve a proportion problem like A:B = C:D where one value is unknown, cross-multiply and solve for the unknown. For example, if 2:3 = 5:x, then 2×x = 3×5, so 2x = 15, and x = 7.5. This means the ratio 2:3 is equivalent to 5:7.5.

References & Disclaimer

Mathematical Disclaimer

This ratio calculator provides accurate mathematical results based on standard ratio operations. Results are presented in simplified form when possible. For educational purposes, we recommend understanding the manual process of ratio calculations in addition to using this calculator.

References

Math is Fun - Ratios - Comprehensive guide to understanding and working with ratios
Khan Academy - Ratios and Rates - Video tutorials and practice exercises for ratio calculations
Calculator Soup - Ratio Calculators - Additional resources and examples for ratio calculations

Accuracy Notice

This calculator performs calculations using standard JavaScript floating-point arithmetic, which may have minor precision limitations for extremely large or complex ratios. For academic or professional use, verify important calculations manually or with specialized mathematical software.

About the Author

Kumaravel Madhavan

Web developer and data researcher creating accurate, easy-to-use calculators across health, finance, education, and construction and more. Works with subject-matter experts to ensure formulas meet trusted standards like WHO, NIH, and ISO.

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math arithmetic ratio formula calculation

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