Ratio Calculator
Simplify ratios, solve proportions, and find equivalent ratios with our free Ratio Calculator. Perfect for math homework, cooking recipes, mixing ratios, and everyday calculations.
What Is a Ratio?
A ratio is a comparison of two or more quantities, showing the relative sizes of each. Ratios are typically written in the form A:B (e.g., 2:3), meaning for every 2 units of A, there are 3 units of B. Ratios are used in everyday life — from cooking recipes to mixing paint, from financial analysis to image sizing.
This ratio calculator handles three common tasks: simplifying ratios to their lowest terms, solving proportions (finding a missing value in A:B = C:D), and generating equivalent ratios by scaling.
How Does the Ratio Calculator Work?
The calculator uses standard mathematical methods:
Simplify Ratio: Divide both terms by their greatest common divisor (GCD).
Solve Proportion: Cross-multiply: A × D = B × C, then solve for the missing value.
Equivalent Ratio: Multiply both terms by a scale factor.
You can also view the ratio as a fraction, decimal, or percentage for additional context.
Why Use This Ratio Calculator?
- Three Modes: Simplify, solve proportions, or find equivalent ratios.
- Multiple Formats: See the result as a ratio, fraction, decimal, and percentage.
- Visual Representation: A bar chart shows the relative proportions.
- Step-by-Step: Optional steps show how the calculation is performed.
- Free & Private: No registration, no data storage.
Common Uses for Ratios
- Cooking & Recipes: Scaling ingredients up or down (e.g., 2 cups flour : 1 cup sugar).
- Mixing: Paint, concrete, or chemical mixtures (e.g., 1:4 ratio of paint to water).
- Finance: Financial ratios like debt-to-equity or price-to-earnings.
- Design & Photography: Aspect ratios for images and screens (e.g., 16:9).
- Education: Solving math problems and learning proportional reasoning.
❓ Ratio Calculator FAQ
What is a ratio?
A ratio is a way to compare two or more quantities. It shows how much of one thing there is compared to another. For example, a ratio of 2:3 means for every 2 units of the first quantity, there are 3 units of the second.
How do I simplify a ratio?
To simplify a ratio, divide both terms by their greatest common divisor (GCD). For example, 12:18 simplifies to 2:3 because the GCD of 12 and 18 is 6 (12÷6=2, 18÷6=3).
What is a proportion?
A proportion is an equation that states that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios simplify to 2:3.
How do I solve a proportion?
To solve a proportion like A:B = C:D, cross-multiply: A × D = B × C. Then solve for the unknown value. For example, if 2:3 = 4:x, then 2x = 12, so x = 6.
What is an equivalent ratio?
Equivalent ratios are ratios that have the same value when simplified. For example, 2:3, 4:6, and 6:9 are all equivalent ratios. You can find equivalent ratios by multiplying or dividing both terms by the same number.
How do I find an equivalent ratio?
Multiply both terms of the ratio by the same scale factor. For example, to find an equivalent ratio to 2:3 with a scale factor of 4, multiply both terms by 4 to get 8:12.
What is the difference between a ratio and a fraction?
A ratio compares two quantities (A:B), while a fraction represents a part of a whole (A/B). However, a ratio can be expressed as a fraction (A/B) and vice versa. For example, the ratio 2:3 can be written as the fraction 2/3.
How do I convert a ratio to a percentage?
To convert a ratio A:B to a percentage, first write it as a fraction A/B, then multiply by 100. For example, 2:3 = 2/3 × 100 = 66.67%.
What is a part-to-part ratio?
A part-to-part ratio compares two parts of a whole. For example, if a class has 12 boys and 18 girls, the part-to-part ratio of boys to girls is 12:18 (simplified to 2:3).
What is a part-to-whole ratio?
A part-to-whole ratio compares one part to the total. For example, if a class has 12 boys out of 30 students, the part-to-whole ratio is 12:30 (simplified to 2:5).
How do I use ratios in cooking?
Recipes often use ratios to specify ingredient proportions. For example, a 2:1 ratio of flour to sugar means for every 2 cups of flour, you use 1 cup of sugar. To scale a recipe, multiply or divide all parts of the ratio by the same factor.
What is an aspect ratio?
An aspect ratio is a ratio that describes the proportional relationship between the width and height of an image or screen. Common aspect ratios include 16:9 (widescreen), 4:3 (standard), and 1:1 (square).
How do I calculate the aspect ratio of an image?
Divide the width by the height and simplify the ratio. For example, an image that is 1920 pixels wide and 1080 pixels tall has an aspect ratio of 1920:1080, which simplifies to 16:9.
What is the golden ratio?
The golden ratio (approximately 1:1.618) is a special ratio found in nature, art, and architecture. It's often considered aesthetically pleasing and is used in design and composition.
How do I compare two ratios?
To compare two ratios, convert them to fractions or decimals and compare the values. For example, 2:3 ≈ 0.667 and 3:4 = 0.75, so 3:4 is larger than 2:3.
What is the greatest common divisor (GCD) and how does it relate to ratios?
The GCD is the largest number that divides evenly into both terms of a ratio. To simplify a ratio, divide both terms by their GCD. For example, the GCD of 12 and 18 is 6, so 12:18 simplifies to 2:3.
Can ratios have decimals?
Yes, ratios can have decimal values. For example, 2.5:3.5 is a valid ratio. However, ratios are often expressed as whole numbers for simplicity. This calculator accepts decimals and can simplify them.
What is a scale factor in ratios?
A scale factor is a number that you multiply both terms of a ratio by to create an equivalent ratio. For example, with a scale factor of 3, the ratio 2:3 becomes 6:9.