Ratio and Proportion Calculator

Calculate ratios, proportions, and solve for unknown values in proportional relationships. This tool helps you compare quantities and find missing values in proportion problems.

First Value (A) Enter the first value in the ratio A:B

Second Value (B) Enter the second value in the ratio A:B

Calculation Type Select what type of calculation you want to perform

Third Value (C) Enter the third value for proportion calculations (if applicable)

Fourth Value (D) Enter the fourth value for ratio comparison (if applicable)

Scale Factor Enter the factor to scale your ratio (if applicable)

Decimal Precision: 2 Number of decimal places in results

Show Calculation Steps

Display the step-by-step calculation process

Quick Examples:

How to Use This Calculator

Enter the values for your ratio (A and B)
Select the type of calculation you want to perform
Enter additional values as required by your calculation type
Adjust the decimal precision for your results
Click "Calculate" to see your results and calculation steps

Formula Used

A:B = C:D (Proportion)

x = (B × C) ÷ A (Finding Missing Value)

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

Where:

A, B, C, D = Values in the proportion
x = Unknown value to be calculated
GCD = Greatest Common Divisor

Example Calculation

Real-World Scenario:

A recipe calls for 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?

Given:

2 cups of flour for 12 cookies (A:B = 2:12)
Want to make 30 cookies (C = 30)
Need to find x = cups of flour for 30 cookies

Calculation:

2:12 = x:30

x = (12 × 30) ÷ 2 = 360 ÷ 2 = 180

Wait, that's not right. Let's fix the formula:

2:12 = x:30

x = (2 × 30) ÷ 12 = 60 ÷ 12 = 5

Result: 5 cups of flour are needed to make 30 cookies.

Why This Calculation Matters

Practical Applications

Scaling recipes for different serving sizes
Converting measurements between different units
Calculating map distances and real distances
Determining ingredient proportions in manufacturing

Key Benefits

Maintains consistent relationships between quantities
Helps in scaling up or down while preserving proportions
Essential for accurate measurements in many fields
Fundamental concept in mathematics and everyday problem-solving

Common Mistakes & Tips

When solving A:B = C:D for an unknown, remember to multiply the known value opposite the unknown. For example, if solving for x in A:B = C:x, the correct formula is x = (B × C) ÷ A, not x = (A × C) ÷ B.

The order of values in a ratio matters. A:B is not the same as B:A. When setting up proportions, make sure the corresponding values are in the same position. For example, if comparing apples to oranges, keep apples as the first value in all ratios.

Always simplify ratios to their lowest terms by dividing both values by their greatest common divisor. This makes the ratio easier to understand and work with. For example, 8:12 should be simplified to 2:3.

Frequently Asked Questions

A ratio compares two quantities (A:B), while a proportion states that two ratios are equal (A:B = C:D). A proportion can be used to solve for an unknown value when three values are known.

The GCD is the largest number that divides both values without a remainder. For small numbers, you can find it by listing factors. For larger numbers, the Euclidean algorithm is efficient: GCD(a,b) = GCD(b, a mod b), repeat until b = 0.

Yes, ratios can have more than two values, such as A:B:C. These are often used to compare three or more quantities. For example, a concrete mix might have a ratio of 1:2:3 (cement:sand:gravel).

References & Disclaimer

Mathematical Disclaimer

This calculator provides basic ratio and proportion calculations for educational purposes. Results are based on standard mathematical formulas. For critical applications, verify calculations independently.

References

Math is Fun: Ratios - Introduction to ratios and their applications
Khan Academy: Ratios and Rates - Comprehensive lessons on ratios and proportions
Cuemath: Ratios and Proportions - Detailed explanations with examples

Accuracy Notice

This calculator performs calculations based on the input provided. Results are rounded to the selected decimal precision. For scientific or engineering applications, use specialized software and verify critical calculations.

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 proportion mathematics formula calculation

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