Ratio Calculator
Calculate and simplify ratios instantly. Perfect for cooking, mixing, scaling recipes, and comparing quantities with step-by-step explanations.
How to Use This Calculator
- 1Select the type of ratio calculation you need from the four options.
- 2Enter the numbers in the input fields.
- 3Click "Calculate" to see the result and step-by-step explanation.
- 4Use "Clear" to reset and start over.
Common Use Cases
- Cooking: Scale recipes up or down (2:3 flour to water ratio)
- Mixing: Dilute cleaning solutions or paint (1:4 ratio)
- Finance: Compare investment ratios or debt-to-income
- Design: Maintain aspect ratios when resizing images
The Math Behind Ratios
This calculator uses these mathematical principles:
- • Simplification: Divide both numbers by their GCD
- • Scaling: Multiply both parts by the same factor
- • Equivalence: Cross products are equal if ratios match (a×d = b×c)
Understanding Ratios: A Complete Guide
A ratio is a way to compare two or more quantities by showing how much of one thing there is relative to another. Ratios are fundamental in mathematics and appear in countless real-world applications, from cooking and construction to finance and engineering.
What is a Ratio?
A ratio compares two quantities using division. It can be written in several ways: as a fraction (2/3), with a colon (2:3), or with the word "to" (2 to 3). All three forms mean the same thing: for every 2 units of the first quantity, there are 3 units of the second quantity.
Example: Paint Mixing
If a paint mixture calls for a 2:1 ratio of blue to white paint, this means for every 2 parts blue, you need 1 part white. So if you use 4 cups of blue paint, you need 2 cups of white paint to maintain the ratio.
How to Simplify Ratios
Simplifying a ratio means reducing it to its smallest whole number form while keeping the same relationship. To simplify:
- Find the Greatest Common Divisor (GCD) of both numbers
- Divide both numbers by the GCD
- The result is the simplified ratio
Example: Simplify the ratio 12:18
GCD(12, 18) = 6
12 ÷ 6 = 2, 18 ÷ 6 = 3
Simplified ratio: 2:3
Equivalent Ratios
Two ratios are equivalent if they represent the same relationship. You can create equivalent ratios by multiplying or dividing both parts of a ratio by the same non-zero number. For example, 1:2, 2:4, and 5:10 are all equivalent ratios.
Real-World Applications
Cooking and Baking
Recipes often use ratios. A classic vinaigrette uses a 3:1 ratio of oil to vinegar.
Photography
Aspect ratios like 16:9 (widescreen) or 4:3 (standard) define image proportions.
Finance
Financial ratios compare metrics like debt-to-equity or price-to-earnings.
Construction
Concrete mixing ratios (like 1:2:3 for cement:sand:gravel) ensure proper strength.
Want to Learn More?
Read our comprehensive guide to fraction calculations, which covers ratios in depth with more examples and formulas.
Frequently Asked Questions
How do I simplify a ratio?
To simplify a ratio, find the Greatest Common Divisor (GCD) of both numbers, then divide each number by the GCD. For example, to simplify 12:18, find GCD(12,18) = 6, then divide both by 6 to get 2:3.
What is a ratio used for?
Ratios are used to compare quantities and show the relationship between two or more numbers. Common applications include cooking (recipe ratios), mixing solutions, scaling designs, financial analysis, and map scales.
How do I check if two ratios are equivalent?
Two ratios are equivalent if they simplify to the same ratio, or if the cross products are equal. For example, 2:3 and 4:6 are equivalent because 2×6 = 3×4 (both equal 12), and both simplify to 2:3.
Is this ratio calculator free to use?
Yes, our ratio calculator is completely free to use. No registration or download required. Use it as much as you need for personal, educational, or business purposes.
What is a three-part ratio?
A three-part ratio compares three quantities, written as A:B:C. For example, concrete mix might use a 1:2:3 ratio of cement to sand to gravel. Our calculator can simplify three-part ratios by finding the GCD of all three numbers.
About This Tool
Created by the Calculatify team. We review and update our calculators regularly to ensure accuracy and usefulness. Last reviewed: February 2026.
Based on standard mathematical principles. For educational and general use.