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Home Page > Math > Basic Math Operations > Ratio Calculator

Ratio Calculator

Solve proportions, simplify ratios to lowest terms, scale ratios up or down, and generate equivalent ratios. Free online ratio calculator with step-by-step solutions and visual ratio bars.

Ratio Calculator
⚡ Quick Examples:
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Leave one field empty to solve for it, or fill all four to verify the proportion.

Embed Ratio Calculator Widget

About Ratio Calculator

The Ratio Calculator is a comprehensive tool for working with ratios and proportions. Whether you need to solve for a missing value in a proportion, simplify a ratio to its lowest terms, scale a ratio by a factor, or generate a table of equivalent ratios, this calculator handles it all with visual ratio bars and step-by-step solutions.

What is a Ratio?

A ratio is a comparison of two or more quantities that shows their relative sizes. Written as a:b (read "a to b"), it tells you how much of one thing there is compared to another. For example, if a recipe calls for flour and sugar in a 3:1 ratio, you use 3 parts flour for every 1 part sugar.

Ratios can involve more than two quantities. A ratio of 2:3:5 means the first quantity is 2 parts, the second is 3 parts, and the third is 5 parts out of a total of 10 parts.

Key Ratio Formulas

Cross Multiplication (Proportion Solving)
If \(\frac{a}{b} = \frac{c}{d}\), then a × d = b × c
Simplifying a Ratio
a:b → \(\frac{a}{\gcd(a,b)}\) : \(\frac{b}{\gcd(a,b)}\)

How to Use This Calculator

  1. Select an operation mode: Choose from Solve Proportion, Simplify, Scale, or Equivalents using the tabs at the top.
  2. Enter your values: For Solve, enter three values and leave one blank. For Simplify, enter a ratio like 12:8. For Scale, enter a ratio and a multiplier. For Equivalents, enter a ratio and the number of equivalents to generate.
  3. Click Calculate: Press the Calculate button to process your input.
  4. Review results: View the answer with animated visual ratio bars showing proportions, step-by-step solution breakdown, and simplified forms.

Types of Ratio Problems

Solving Proportions

A proportion is an equation stating two ratios are equal: a:b = c:d. If one value is unknown, cross multiplication solves it. For example, if 2:3 = x:9, then 3x = 18, so x = 6.

Simplifying Ratios

To simplify a ratio, divide all parts by their greatest common divisor (GCD). For example, 12:8 has GCD = 4, so it simplifies to 3:2. This works for multi-part ratios too: 10:15:25 has GCD = 5, simplifying to 2:3:5.

Scaling Ratios

Scaling a ratio means multiplying all parts by the same factor. If a recipe for 4 servings uses a 2:1 flour-to-butter ratio and you need 12 servings (factor of 3), the scaled ratio is 6:3.

Equivalent Ratios

Equivalent ratios express the same relationship with different numbers. The ratios 1:2, 2:4, 3:6, and 4:8 are all equivalent because they all simplify to 1:2.

Real-World Applications of Ratios

FieldApplicationExample
CookingRecipe scalingFlour to sugar = 3:1
MapsScale representation1:50,000 (1 cm = 500 m)
FinanceDebt-to-income ratioMonthly debt:income = 1:3
ScienceMixing solutionsAcid:water = 1:9
ArchitectureScale modelsModel:actual = 1:100
PhotographyAspect ratioWidth:height = 16:9

Frequently Asked Questions

What is a ratio?

A ratio is a comparison of two or more quantities that shows their relative sizes. It is written as a:b (or a:b:c for three quantities) and indicates how many times one value contains or is contained within the other. For example, 3:2 means for every 3 units of the first quantity, there are 2 units of the second.

How do you solve a proportion?

To solve a proportion a/b = c/d with one unknown, use cross multiplication: a times d = b times c. Then isolate the unknown variable. For example, to solve 2/3 = x/9, cross multiply to get 3x = 18, so x = 6.

What does it mean to simplify a ratio?

Simplifying a ratio means reducing it to its smallest whole number form by dividing all parts by their greatest common divisor (GCD). For example, 12:8 simplifies to 3:2 because the GCD of 12 and 8 is 4, and dividing both by 4 gives 3:2.

How do you find equivalent ratios?

To find equivalent ratios, multiply or divide all parts of the ratio by the same non-zero number. For example, equivalent ratios of 2:3 include 4:6, 6:9, 8:12, and so on. All equivalent ratios represent the same proportion.

What is the difference between a ratio and a proportion?

A ratio compares two or more quantities (e.g., 3:4), while a proportion is an equation stating that two ratios are equal (e.g., 3:4 = 6:8). A proportion always involves two ratios connected by an equals sign.

Common Ratios

16:94:321:93:25:41.85:12.35:116:109:161:12:310:166:48:512:920:15

Reference this content, page, or tool as:

"Ratio Calculator" at https://MiniWebtool.com/ratio-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Mar 20, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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