Ratio Calculator – Simplify, Scale, Compare, and Convert Ratios

  • Adam
  • November 4, 2025

Free online ratio calculator for simplifying ratios, scaling ratios, comparing ratios, finding missing values in proportions, and converting ratios to decimal and percentage formats with step-by-step solutions.

Ratio Calculator

Advanced Tool for Simplifying, Scaling, and Comparing Ratios

Quick Navigation

Simplify Ratio

Reduce ratio to simplest form

Scale Ratio

Multiply ratio by a factor

Compare Ratios

Check if two ratios are equivalent

Find Missing Value

Solve for missing value in proportion: A:B = C:D

Convert Ratio Format

Convert ratio to different formats

What is a Ratio?

A ratio is a mathematical comparison of two or more quantities showing their relative sizes. Ratios express how much of one thing there is compared to another. For example, if a class has 12 boys and 18 girls, the ratio of boys to girls is 12:18, which simplifies to 2:3.

Ratios can be written in three different ways: as "a to b" (2 to 3), with a colon "a:b" (2:3), or as a fraction "a/b" (2/3). All three representations mean the same thing. Ratios are fundamental in mathematics, appearing in recipes, maps, scale drawings, business analysis, and countless other applications.

Understanding ratios is crucial for working with proportions, rates, percentages, and scaling. When you scale a recipe, adjust a drawing, or analyze data, you're using ratios. This calculator helps you simplify, scale, compare, and convert ratios with complete step-by-step explanations.

Key Concept: A ratio shows a relationship between quantities. Equivalent ratios (like 2:3 and 4:6) represent the same relationship even though the numbers differ.

Key Features & Capabilities

This comprehensive ratio calculator provides multiple calculation modes and detailed analysis:

📉 Simplify Ratios Reduce any ratio to its simplest form using greatest common divisor
📈 Scale Ratios Multiply ratios by any factor to find equivalent ratios at different scales
🔄 Compare Ratios Determine if two ratios are equivalent or which is greater
❓ Find Missing Value Solve proportions using cross multiplication for unknown values
🔢 Format Conversion Convert ratios to decimal, percentage, and fraction representations
📋 Step-by-Step Solutions See detailed breakdown showing how each calculation is performed
✓ GCD Calculation Displays greatest common divisor for simplification
📊 Statistical Analysis View related values and equivalent ratios
📋 Copy to Clipboard One-click copy functionality to transfer results to other applications
🎓 Educational Content Comprehensive guides and examples explaining ratio concepts
⚡ Real-Time Calculation Instant results with no delays or external dependencies
📱 Fully Responsive Works seamlessly on desktop, tablet, and mobile devices

How to Use This Calculator

Step-by-Step Guide

  1. Choose Your Operation: Select the appropriate tab: Simplify (reduce ratio), Scale (multiply ratio), Compare (check equivalence), Missing Value (solve proportion), or Convert (change format).
  2. Enter Your Values: Input the numbers for your ratio. For simplify and scale, enter both values. For compare, enter two complete ratios. For missing value, enter three known values.
  3. Specify Parameters: For scaling, enter the multiplication factor. For missing value, leave the unknown blank.
  4. Click Calculate: Press the Calculate button to perform the computation using ratio formulas.
  5. Review Results: The main result displays prominently in the appropriate format.
  6. Study the Steps: Below the result, see detailed breakdown showing the calculation method.
  7. Analyze Statistics: See related values like GCD, decimals, percentages, or equivalent ratios.
  8. Copy or Clear: Use Copy to transfer results. Use Clear to reset for a new calculation.

Tips for Accurate Use

  • Positive Numbers: Ratios work with positive numbers. Both values should be greater than zero.
  • Order Matters: In ratios, order is important. 2:3 is different from 3:2. Read ratio descriptions carefully.
  • Simplest Form: A simplified ratio has no common factors other than 1. For example, 12:18 simplifies to 2:3.
  • Equivalent Ratios: Many ratios are equivalent to the same ratio. 2:3, 4:6, 6:9, and 8:12 are all equivalent.
  • Cross Multiplication: For proportions a:b = c:d, cross multiply: a×d = b×c. Use this to find missing values.

Complete Formulas Guide

Simplifying Ratios

Finding Simplest Form
Simplified Ratio = A ÷ GCD : B ÷ GCD

Where GCD is the Greatest Common Divisor of A and B

Example: Simplify 12:18
GCD(12, 18) = 6
Simplified = 12÷6 : 18÷6 = 2:3

Scaling Ratios

Multiplying by Scale Factor
Scaled Ratio = (A × Factor) : (B × Factor)

Example: Scale 2:3 by factor of 5
= (2×5) : (3×5) = 10:15

Comparing Ratios

Cross Multiplication Comparison
For ratios A:B and C:D
Calculate: A×D and B×C

If A×D = B×C: ratios are equivalent
If A×D > B×C: first ratio is larger
If A×D < B×C: second ratio is larger

Example: Compare 2:3 and 4:6
2×6 = 12 and 3×4 = 12
Result: Equivalent ratios

Proportion - Missing Value

Cross Multiplication for Unknown
If A:B = C:D, then A×D = B×C

Solving for D (unknown):
D = (A×C) / B

Example: If 2:3 = 4:D
2×D = 3×4
2D = 12
D = 6

Ratio to Decimal and Percentage

Format Conversions
Decimal = A / B
Percentage = (A / (A+B)) × 100%

Example: For 3:4
Decimal = 3/4 = 0.75
Percentage = (3/7) × 100% ≈ 42.86%

Real-World Applications

Cooking and Recipes

Recipes use ratios for ingredient proportions. Scaling a recipe requires multiplying all ingredients by the same ratio factor to maintain the correct balance and taste.

Maps and Scale Drawings

Maps use ratios to show scale. A 1:100,000 ratio means 1 unit on the map represents 100,000 units in reality. This allows representing large areas on manageable paper.

Photography and Art

Aspect ratios (like 16:9 for widescreen) define proportions of images. Understanding ratios helps maintain proper proportions when resizing artwork or photographs.

Business and Finance

Financial ratios compare different metrics: profit margin (profit:revenue), debt ratio (debt:assets), and return ratios. These help analyze company performance and health.

Statistics and Data

Ratios compare populations, frequencies, and proportions in data. They help visualize relationships and make comparisons between different groups.

Construction and Engineering

Ratios determine material mixtures (concrete ratios), structural proportions, and scale models. Maintaining correct ratios ensures structural integrity and safety.

Worked Examples

Example 1: Simplifying a Ratio

Problem: Simplify the ratio 24:36

Solution:
Find GCD(24, 36):
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
GCD = 12

Divide both by 12:
24 ÷ 12 : 36 ÷ 12 = 2:3

Example 2: Scaling a Ratio

Problem: Scale the ratio 3:5 by a factor of 4

Solution:
Multiply both values by 4:
(3 × 4) : (5 × 4) = 12:20

This maintains the same relationship while increasing the quantities

Example 3: Comparing Ratios

Problem: Are the ratios 2:5 and 4:10 equivalent?

Solution:
Use cross multiplication:
2 × 10 = 20
5 × 4 = 20

Since 20 = 20, the ratios ARE EQUIVALENT
(4:10 is just 2:5 scaled by 2)

Example 4: Finding Missing Value

Problem: If 3:4 = 9:x, find x

Solution:
Using proportion: 3:4 = 9:x
Cross multiply: 3 × x = 4 × 9
3x = 36
x = 36 ÷ 3 = 12

Verification: 3:4 = 9:12
Cross multiply: 3×12 = 36 and 4×9 = 36 ✓

Example 5: Converting Ratio Format

Problem: Convert the ratio 1:4 to decimal and percentage

Solution:
Ratio notation: 1:4
Fraction: 1/4
Decimal: 1 ÷ 4 = 0.25
Percentage: (1/(1+4)) × 100% = (1/5) × 100% = 20%

Frequently Asked Questions

❓ What's the difference between ratio and proportion?
A ratio compares two quantities (2:3). A proportion states that two ratios are equal (2:3 = 4:6). Ratios are the building blocks; proportions use ratios to solve problems with missing values.
❓ Can I have a ratio of 0:5?
No. Ratios require positive numbers. Zero ratios don't make mathematical sense in most contexts. Both values should be greater than zero.
❓ Is 2:3 the same as 3:2?
No. Order matters in ratios. 2:3 means "for every 2 of the first, there are 3 of the second." 3:2 reverses this relationship. They represent different comparisons.
❓ How do I scale a recipe using ratios?
Find the scale factor by dividing desired quantity by original quantity. Multiply all ingredients by this factor. Example: To double a recipe, multiply all ingredients by 2.
❓ What is equivalent ratio?
Equivalent ratios represent the same relationship. 1:2, 2:4, 3:6, and 5:10 are equivalent because they simplify to the same ratio. Multiply or divide both parts by the same number to find equivalents.
❓ Can I have three-part ratios like 2:3:5?
Yes! Three-part ratios compare three quantities. For example, in a paint mixture 2:3:5, use 2 parts red, 3 parts blue, and 5 parts yellow. Each part maintains the same scale.
❓ How do I convert a ratio to a percentage?
For ratio a:b, the percentage of the first part is [a/(a+b)] × 100%. Example: For 1:4, percentage = [1/5] × 100% = 20%.
❓ What is the relationship between ratios and fractions?
A ratio a:b can be written as the fraction a/b. However, a ratio compares quantities while a fraction represents a part of a whole. The key difference is in interpretation.
❓ Can ratios have decimal numbers?
Yes! Ratios can include decimals or fractions. For example, 2.5:3.75 or 1/2:3/4 are valid ratios. The same rules apply for simplification and comparison.
❓ When would I use this calculator?
Use for: scaling recipes, interpreting maps, resizing images, analyzing business metrics, solving math homework, comparing data, creating scale models, or any situation involving proportional relationships.

Start Working with Ratios

Whether you're scaling a recipe, interpreting a map, resizing an image, analyzing data, or solving math problems, this comprehensive ratio calculator helps you understand and work with proportional relationships. Fast, accurate, and completely free.

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