Ratio Calculator: Simplify and Compare

What Is a Ratio?

A ratio compares two or more quantities by showing how much of one quantity exists relative to another. Ratios are commonly written using a colon, such as 2:3, or as a fraction, such as 2/3.

A ratio does not necessarily represent a total amount. Instead, it describes the relationship between quantities. For example, a ratio of 2:3 means that for every 2 units of the first quantity, there are 3 units of the second quantity.

Use the calculator above to simplify a ratio, compare its parts, and generate equivalent values. When you need to work with related calculations, the fraction tools helps with fraction operations, while the percentage tools converts values into percentages and calculates percentage changes.

How to Calculate a Ratio

To write a ratio, place the quantities in the same order in which you want to compare them. If there are 10 red objects and 15 blue objects, the ratio of red to blue is 10:15.

A ratio can then be simplified by dividing both parts by their greatest common divisor. For 10:15, the greatest common divisor is 5, so both numbers can be divided by 5 to produce the simplified ratio 2:3.

Dividing both parts by the same nonzero number does not change the relationship represented by the ratio. It simply expresses that relationship using smaller numbers.

Ratio Examples

These ratios look different because their numbers are different, but they all represent the same relationship. Each can be reduced to 2:3.

Understanding Equivalent Values

Equivalent ratios are ratios that represent the same relationship even though their numbers are different. You can create an equivalent ratio by multiplying or dividing every part of the ratio by the same nonzero number.

For example, multiplying both parts of 2:3 by 4 gives 8:12. Because both values were multiplied by the same number, the relationship remains unchanged.

Equivalent ratios are particularly useful when scaling recipes, adjusting quantities, comparing measurements, creating models, or solving proportion problems.

Ratios and Fractions

A two-part ratio can also be written as a fraction. A ratio of 2:5 can be represented as 2/5 when the purpose is to compare the first quantity with the second quantity.

However, the meaning depends on the wording of the question. The ratio 2:5 describes a relationship between two quantities, while the fraction 2/5 can describe the first quantity as a portion of the second quantity.

If you need to perform calculations involving fractions, our fraction calculations can be useful alongside the Ratio Calculator.

Converting a Ratio to a Percentage

A ratio can be converted into a percentage when you want to understand one part as a share of a total. For a ratio of 2:3, the total number of parts is 2 + 3 = 5.

The first quantity therefore represents 2 out of 5 parts, while the second quantity represents 3 out of 5 parts.

For a 2:3 ratio, the first part is 40% of the total and the second part is 60% of the total. The two percentages add to 100%.

This is different from simply interpreting 2:3 as 2/3. When converting a ratio into shares of the total, the denominator is the sum of all ratio parts.

This distinction is especially important when working with proportions, survey results, budgets, ingredients, and other situations where the parts make up a complete total. Our percentage calculations can also help with percentage calculations.

How to Find a Missing Value in a Ratio

If two ratios are equivalent and one value is missing, you can use proportional relationships to find the missing number.

For example, suppose 2:3 is equivalent to x:12. Since 3 must be multiplied by 4 to become 12, 2 must also be multiplied by 4. Therefore, x is 8.

The key principle is that both sides of the ratio must be scaled by the same factor. If one quantity is multiplied by 4, the corresponding quantity must also be multiplied by 4.

Ratios in Everyday Life

Ratios are used in many practical situations. Recipes use ratios to maintain the correct relationship between ingredients. Maps use scale ratios to represent large distances on smaller surfaces. Businesses use ratios to compare financial and operational measurements.

Ratios can also be used to describe mixtures. If a solution requires a 1:4 ratio of concentrate to water, one part concentrate is combined with four parts water. Increasing the batch size does not change the ratio as long as both quantities are scaled together.

Ratios in recipes

Suppose a recipe uses 2 cups of flour for every 3 cups of another ingredient. The ratio is 2:3. If you want to double the recipe, multiply both parts by 2, producing 4:6.

The numbers increase, but the relationship between the ingredients remains exactly the same.

Ratios in maps and scale drawings

A map scale can be expressed as a ratio between a distance on the map and the corresponding real-world distance. Maintaining that ratio allows a small drawing to represent a much larger area.

Ratios in business

Businesses often compare quantities using ratios. Examples include revenue per employee, current assets compared with liabilities, or one expense category compared with total spending.

Ratio vs. Proportion

A ratio describes a relationship between quantities, while a proportion states that two ratios are equal. For example, 2:3 is a ratio, while 2:3 = 8:12 is a proportion.

Proportions are useful when a known relationship needs to be scaled to a different quantity. The calculator above can help you understand the underlying relationship before solving a proportional problem. For an additional lesson with worked examples, see Khan Academy's ratios and proportions lessons.

Part-to-Part vs. Part-to-Whole Ratios

A part-to-part ratio compares one component directly with another component. For example, a class with 12 boys and 18 girls has a boys-to-girls ratio of 12:18, which simplifies to 2:3.

A part-to-whole ratio compares one component with the total. In the same class, there are 30 students, so the boys-to-total ratio is 12:30, which simplifies to 2:5.

How to Simplify a Ratio

To simplify a ratio, find the greatest common divisor shared by all of its values. Divide every value by that divisor.

1. Write the ratio in its original form.
2. Find the greatest common divisor.
3. Divide every part by the divisor.
4. Write the resulting simplified ratio.

For example, consider 36:48. The greatest common divisor is 12. Dividing both values by 12 gives 3:4. Therefore, 36:48 and 3:4 represent the same relationship.

Common Ratio Mistakes

One common mistake is changing only one side of a ratio. When creating an equivalent ratio, every part must be multiplied or divided by the same factor.

Another mistake is reversing the order of the ratio. A ratio of 2:3 is not the same as 3:2. The first number describes the first quantity and the second number describes the second quantity.

It is also important to distinguish a part-to-part ratio from a part-to-whole ratio. If two quantities are in a 2:3 ratio, there are 5 total parts, not 3 total parts.

Tips for Accurate Results

• Keep the quantities in the correct order.
• Use the same units before comparing quantities.
• Divide every part by the same factor when simplifying.
• Use the greatest common divisor to obtain the simplest whole-number ratio.
• Remember that a part-to-whole ratio uses the sum of all parts as the whole.
• Do not reverse a ratio unless you also reverse the meaning of the comparison.

Frequently Asked Questions