Ratio Calculator

Written by Aarav Sharma, Mathematics Editor Reviewed by Vikram Sen, Technical Reviewer Last updated: June 1, 2026 Last verified: June 1, 2026 · Methodology · Accuracy policy

Simplify a two-part ratio with the greatest common divisor and show Part A as a percent of A+B.

simplified ratio via GCD; Part A share % = A ÷ (A + B) × 100.

Tip: Keep both parts in the same units so the simplified ratio stays meaningful.

Cluster: Ratios hub · Complete percentage guide

Two-part ratios and their percent view. Enter the two numbers that form a ratio (for example 12 and 16); the tool simplifies the pair and shows each side as a percent of the combined total. It is about relative parts, not currency growth over time.

Not the same as proportional split , which takes a dollar pool and ratio weights, or ratio to percentage when you only need the conversion pattern from the conversions cluster.

Use first and second values below. For market-level revenue share, use market share .

Simplified Ratio

Original Ratio:*

Simplified:*

As Percentage:*

Understanding Ratios

Ratios express relationships between quantities. They're fundamental to cooking, chemistry, finance, and countless other fields. Unlike percentages, ratios show relative amounts without reference to a whole.

Ratio Types

Part-to-Part: 3:2 compares two components
Part-to-Whole: 3:5 where one is subset of other
Equivalent Ratios: 1:2 = 2:4 = 50:100

Simplifying Ratios

Divide all parts by their GCD (Greatest Common Divisor). 12:18 simplifies to 2:3. Ratios with decimals can be multiplied to whole numbers: 1.5:2 = 3:4. Expressing ratios in simplest form makes comparison and scaling easier.

Complete Guide to Understanding Ratios

How we calculate. Simplify A:B by GCD, then Part A share % = A ÷ (A + B) × 100. This is not A ÷ B × 100. See our methodology and accuracy policy .

Real-world scenario: A cook simplified a 12:16 flour-to-water ratio to 3:4 here before scaling the preferment.

What is a Ratio?

A ratio is a mathematical comparison between two or more quantities. It shows the relative size of one value compared to another. Ratios are written with a colon (:) between numbers, such as 3:2 or 4:1.

Think of ratios like a recipe: if a cake requires ingredients in a 2:1 ratio of flour to sugar, you need twice as much flour as sugar. If you use 4 cups of flour, you need 2 cups of sugar.

How to Simplify Ratios

Simplifying a ratio is similar to simplifying a fraction. You divide both numbers by their Greatest Common Divisor (GCD) to get the smallest whole numbers that maintain the same proportion.

The worked example for ratio calculator was verified with the calculator form on this page—enter the same values to confirm the result.

Given: Example: Simplify 12:16

Step 1: Find GCD of 12 and 16 → GCD = 4

Step 2: Divide both by 4 → 12÷4 = 3, 16÷4 = 4

Result: 3:4 (simplified form)

Both 12:16 and 3:4 represent the exact same proportion!

Converting Ratios to Percentages

To convert a ratio to percentages, you need to determine what portion each part represents of the total. This is incredibly useful for understanding proportions at a glance.

Ratio to Percentage Formula

Percentage = (Part / Total) × 100

Where Total = Sum of all parts in the ratio

Example: Convert 3:2 to percentages

Step 1: Calculate total → 3 + 2 = 5 parts

Step 2: First part → (3/5) × 100 = 60%

Step 3: Second part → (2/5) × 100 = 40%

Verify: 60% + 40% = 100% ✓×

Real-World Applications

Example 1: Recipe Scaling

Scenario: A recipe uses flour, sugar, and butter in a 3:2:1 ratio

Total parts = 3 + 2 + 1 = 6

Flour: (3/6) × 100 = 50% of the mixture

Sugar: (2/6) × 100 = 33.33% of the mixture

Butter: (1/6) × 100 = 16.67% of the mixture

If you want to make 600g total, you'd use: 300g flour, 200g sugar, 100g butter.

Example 2: Investment Portfolio

Scenario: Divide $10,000 between stocks and bonds in a 4:1 ratio

Total parts = 4 + 1 = 5

Stock portion: (4/5) = 0.8 or 80%

Stocks: 0.8 × $10,000 = $8,000

Bonds: 0.2 × $10,000 = $2,000

Example 3: Color Mixing

Scenario: Mix paint colors red:blue:yellow in ratio 5:3:2

Total parts = 5 + 3 + 2 = 10

Red: 50%, Blue: 30%, Yellow: 20%

For 1 liter: 500ml red, 300ml blue, 200ml yellow

🔍 Common Ratios Quick Reference

Original Ratio	Simplified	First Part %
2:2	1:1	50%
6:4	3:2	60%
9:6	3:2	60%
10:5	2:1	66.67%
12:16	3:4	42.86%
15:10	3:2	60%

Order matters: A ratio of 3:2 is NOT the same as 2:3 – they represent opposite proportions
Always simplify: Express ratios in their simplest form (e.g., 10:15 should be 2:3)
Unit consistency: Both quantities must be in the same units before comparing
Verify percentages: When converting to %, all parts should sum to × 100%
Equivalent ratios: Multiplying or dividing both parts by the same number creates an equivalent ratio (2:3 = 4:6 = 6:9)
Proportional relationships: If one part doubles, the other must double to maintain the ratio
Zero values: Ratios with zero (like 0:5) indicate the complete absence of one component

Common Mistakes to Avoid

Mixing units: Comparing 5 inches to 2 feet without converting to the same unit
Forgetting to simplify: Leaving ratios like 20:30 instead of simplifying to 2:3
Reversing the order: Writing 2:5 when you meant 5:2
Incorrect percentage calculation: Dividing by only one part instead of the total

Limitations: ratio calculator results are estimates for learning and quick checks—not financial, legal, tax, or medical advice. Policies, grading scales, and local rules may differ; confirm outcomes with official sources before making decisions.

When to use this calculator

Use this page when two parts should be simplified and shown as shares of the combined total.
Use proportional split to divide a dollar pool by weights.
Use ratio to percentage when conversion wording matters more than simplification.

Still unsure about ratio? Start with the quick answer above, then open the linked calculator that matches your wording.

❓ Frequently Asked Questions

How do ratios represent relationships between quantities?

A ratio is a way to compare two or more numbers. It shows how many times one number contains another.

How do I simplify a ratio?

Divide all numbers in the ratio by their greatest common divisor (GCD). For example, 10:20 simplifies to 1:2.

Can ratios have more than two parts?

Yes, you can have ratios with three or more parts, such as 1:2:3, commonly used in recipes or mixing materials.

🔍 Authoritative References

For more information about ratio and proportion calculations, consult these trusted sources:

SEC EDGAR - Public company financial filings
U.S. Census Bureau - Demographic and economic data