Ratio Calculator
Ratio Calculator
Solve Proportion
Find the missing value in a proportion: A:B = C:D
Result
Common Ratios
Related Tools
What is a Ratio Calculator?
A ratio calculator is a powerful mathematical tool that helps you work with ratios and proportions. Ratios express the relationship between two quantities, showing how many times one value contains another. Our free online ratio calculator can solve proportions, simplify ratios, compare ratios, and scale values.
Ratios are fundamental in mathematics and appear in many real-world applications including cooking, photography, finance, architecture, and science. Understanding ratios helps you scale recipes, calculate aspect ratios, determine mixing proportions, and solve many practical problems.
This calculator provides four key functions: solving for unknown values in proportions (A:B = C:D), simplifying ratios to their lowest terms, comparing two ratios to check if they're equivalent, and scaling ratios by any factor.
Understanding Ratios and Proportions
What is a Ratio?
A ratio compares two quantities by division. It shows how much of one thing there is compared to another.
Example: A ratio of 3:2 means for every 3 of the first quantity, there are 2 of the second.
What is a Proportion?
A proportion states that two ratios are equal. It can be written as A:B = C:D or A/B = C/D.
Cross multiplication: A × D = B × C
Example: 2:3 = 4:6 because 2×6 = 3×4 = 12
Simplifying Ratios
Divide both parts of the ratio by their Greatest Common Divisor (GCD).
Example: 15:25 → GCD is 5 → 15÷5 : 25÷5 = 3:5
Scaling Ratios
Multiply both parts by the same number to maintain the proportion.
Example: 2:3 × 4 = 8:12 (still equivalent to 2:3)
Calculator Features
Solve Proportions
- Find missing value in A:B = C:D
- Solve for any of the four values
- Uses cross multiplication
- Shows the complete proportion
Other Functions
- Simplify ratios to lowest terms
- Compare two ratios for equivalence
- Scale ratios by any factor
- Copy results to clipboard
Frequently Asked Questions
How do I solve for a missing value in a proportion?
Use the Solve tab to find the missing value. Enter the three known values, select which value you want to solve for (A, B, C, or D), and click Solve. The calculator uses cross multiplication: in the proportion A:B = C:D, we know that A×D = B×C, so we can solve for any unknown.
What does it mean to simplify a ratio?
Simplifying a ratio means reducing it to its smallest whole number form while keeping the relationship the same. For example, 12:8 can be simplified to 3:2 by dividing both numbers by 4 (their greatest common divisor). The simplified ratio is easier to understand and work with.
How do I know if two ratios are equivalent?
Two ratios are equivalent if they simplify to the same value. Use the Compare tab to check - enter both ratios and the calculator will tell you if they're equivalent. Mathematically, A:B = C:D if A/B = C/D (the decimal values are equal) or if A×D = B×C (cross multiplication).
What is ratio scaling used for?
Ratio scaling is useful when you need to maintain proportions at a different size. Common uses include: scaling recipes (doubling or halving), resizing images while keeping aspect ratio, mixing ingredients in proportion, and architectural or engineering blueprints where a scale factor is applied.
Common Applications of Ratios
Cooking & Baking
- Scaling recipes up or down
- Mixing ingredients (flour to water)
- Converting serving sizes
Photography & Design
- Aspect ratios (16:9, 4:3)
- Image scaling
- Golden ratio in design (1.618:1)
Finance
- Debt-to-income ratios
- Price-to-earnings ratios
- Investment allocation
Science & Engineering
- Chemical mixing ratios
- Scale models
- Gear ratios