Ratio Calculator

The Ratio Calculator compares quantities multiplicatively. It can reduce a ratio to simplest terms, build an equivalent ratio, or divide a total among parts. A ratio such as 2:3 means the second quantity is one and a half times the first—not that their difference is one.

Part-to-part and part-to-whole are not interchangeable

Reduce whole-number terms by their greatest common factor. To scale a ratio, multiply or divide every term by the same nonzero factor. When sharing a total, add the ratio parts first, find the value of one part, and then multiply.

A ratio a:b is simplified by dividing both terms by their greatest common factor.

Enter the values in their mathematical roles

Enter quantities in the same unit when they describe comparable measurements. Choose whether you are simplifying, scaling, solving an equivalent ratio, or splitting a total. Preserve the order of the terms because 2:5 and 5:2 describe different comparisons.

The governing relationship

A ratio a:b is simplified by dividing both terms by their greatest common factor.

A compact example

18:24 simplifies to 3:4 after both terms are divided by 6.

Valid inputs and boundary cases

Ratios can contain decimals or fractions, but clearing them to whole-number terms often makes the relationship easier to read. Zero may be meaningful in some part-to-part comparisons, although division by a zero reference term is undefined.

Read the answer in context

Use quantities measured in compatible units before comparing them.

An independent check

For equivalent ratios, cross-products must match. For a divided total, add every allocated share and confirm it returns the original amount. Also check the direction: the larger ratio term should receive the larger share.

Errors that change the answer

• Reversing the order of ratio terms
• Reducing only one term
• Comparing quantities in different units
• Dividing a total by the wrong number of parts
• Treating a ratio as a subtraction

Continue with a related calculator

Continue with the Fraction to Decimal Calculator or Proportion Calculator. For everyday arithmetic and order-of-operations checks, use the Basic Calculator.

What this numerical result cannot decide

A ratio expresses relative size, not causation or probability by itself. Mixing recipes, maps, finance, and concentration problems may impose units, safety limits, or definitions that arithmetic alone cannot supply.

A second way to understand the method

If a class has 12 girls and 18 boys, the girl-to-boy ratio is 12:18=2:3. The girl-to-class ratio is 12:30=2:5. Both are correct, but they answer different questions. Label the compared quantities before simplifying.

Scaling a recipe or drawing

If a mix uses water and concentrate in a 4:1 ratio, five total parts make one batch unit. Scaling to 15 liters assigns 12 liters to water and 3 liters to concentrate. For a map scale of 1:50, every drawing length corresponds to fifty of the same real-world units. Labeling the direction prevents an accidental inversion.

Ratios with more than two terms

A three-part ratio such as 2:3:5 contains ten total parts. To divide 240 accordingly, one part is 24, producing shares of 48, 72, and 120. Reduce all terms by a common factor when possible, but never delete a term or change their order because each position names a specific quantity.

Check units before simplifying

A ratio of 2 feet to 8 inches is not 1:4. Convert 2 feet to 24 inches first; the comparable ratio is 24:8=3:1. Unit labels may disappear after a like-unit ratio is reduced, but they are essential during setup.

Ratio Calculator FAQ

How do I simplify 12:18?

Divide both terms by their greatest common factor, 6, to obtain 2:3.

How is a total split in the ratio 2:3?

Divide the total into five equal parts, then allocate two parts and three parts.

Can ratios use different units?

Convert compatible quantities to a common unit before comparing them.

For additional worked mathematics, see the free OpenStax Prealgebra 2e reference.