Simplify Ratio
12:18 = 2:3
Divide both terms by their greatest common divisor.
2:3
Free Online Ratio Calculator
Ratio Calculator with Step-by-Step Results
Simplify ratios, solve proportions, compare equivalent ratios and convert ratio parts into percentages instantly.
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Detailed steps
A:B
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Quick Examples
Common Ratio Calculations
See how ratios can be simplified, compared and converted.
Solve Proportion
2:3 = 4:6
Use cross multiplication to find the missing ratio value.
Equivalent Ratios
2:3 = 4:6
Equal cross products indicate equivalent ratios.
Ratio Percentages
2:3 = 40%:60%
Convert each term into its percentage of the total parts.
Ratio Formulas
Useful Ratio Calculation Formulas
Simplify a Ratio
A:B → (A ÷ GCD):(B ÷ GCD)
Divide both ratio terms by their greatest common divisor.
Equivalent Ratios
A:B = C:D when A × D = B × C
Compare the cross products to test whether two ratios are equivalent.
Solve for D
A:B = C:D → D = (B × C) ÷ A
Rearrange the proportion after cross multiplication.
Ratio to Percentage
A% = A ÷ (A + B) × 100
Divide each term by the total number of parts and multiply by 100.
Ratio Calculator Guide
Free Online Ratio Calculator
Our free online ratio calculator helps you simplify ratios, solve proportions, compare equivalent ratios and convert ratio terms into percentages. Enter your values, choose the required calculation mode and receive an instant result with calculation steps.
Ratios are commonly used in mathematics, education, recipes, maps, design, construction, finance and everyday comparisons. A ratio expresses the relative relationship between two quantities.
What Is a Ratio?
A ratio compares two quantities. It can be written using a colon, such as 2:3, with words such as "2 to 3", or in fraction form as 2/3.
The order of ratio terms matters. The ratio 2:3 does not represent the same ordered comparison as 3:2.
How to Simplify a Ratio
To simplify a ratio of whole numbers, find the greatest common divisor shared by all terms. Divide each term by that common divisor.
Example: Simplify 12:18
GCD of 12 and 18 = 6
12 ÷ 6 = 2
18 ÷ 6 = 3
Simplified ratio = 2:3
What Is a Proportion?
A proportion is an equation stating that two ratios are equal. For example, 2:3 = 4:6 is a proportion because both ratios represent the same relationship.
Proportion problems often contain one unknown value. Cross multiplication can be used to solve for that missing term.
How to Solve a Missing Ratio Value
Suppose the proportion is 2:3 = 4:x. Write it as 2/3 = 4/x and cross multiply. This gives 2x = 12, so x = 6.
2:3 = 4:6
How to Check Equivalent Ratios
Two ratios are equivalent when they represent the same proportional relationship. One common method is cross multiplication.
For 2:3 and 4:6, calculate 2 × 6 and 3 × 4. Both products equal 12, so the ratios are equivalent.
How to Convert a Ratio to Percentages
When ratio terms represent parts of a whole, add the terms to find the total number of parts. Divide each term by the total and multiply by 100.
Example: Convert 2:3 to Percentages
Total parts = 2 + 3 = 5
First part = 2 ÷ 5 × 100 = 40%
Second part = 3 ÷ 5 × 100 = 60%
Result = 40% : 60%
What Does 1:n Mean?
A ratio in 1:n form shows how much of the second quantity corresponds to one unit of the first. To convert A:B into 1:n form, divide both terms by A.
For example, 4:10 becomes 1:2.5 after dividing both terms by 4.
Common Uses of Ratios
Recipes
Scale ingredient quantities while maintaining the same proportions.
Maps & Scale
Compare map distances with corresponding real-world distances.
Business
Compare financial values, costs, sales and performance measures.
Design
Work with image dimensions, layouts and aspect ratios.
Important Note
This calculator is intended for educational, general and informational calculations. Verify critical calculations independently when accuracy is essential.
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FAQ
Frequently Asked Questions
Find the greatest common divisor of the ratio
terms and divide each term by that value.
Write the ratios as equal fractions and use
cross multiplication to solve for the missing value.
Two ratios are equivalent when their cross
products are equal.
Add the terms to find the total number of parts.
Divide each term by the total and multiply by 100.
Yes. Decimal terms can be converted to equivalent
integer terms and then reduced when appropriate.