How to Calculate a Ratio (and Simplify It)

Ratios are everywhere: mixing paint, following a recipe, splitting profits, or reading a map scale. Knowing how to calculate a ratio, and just as importantly how to simplify and scale one, makes all of these tasks straightforward. A ratio simply compares two or more quantities, showing how much of one there is compared to another. This guide explains how to write a ratio, reduce it to its simplest form, scale it up or down while keeping the proportion, and convert it to a fraction or percentage. Each step comes with a clear example. For related proportion work like adjusting recipes, our recipe scaler calculator is a useful tool.

Quick answer: To calculate a ratio, write the two quantities separated by a colon, such as 20:30, then simplify by dividing both by their greatest common factor. 20:30 divides by 10 to become 2:3. To scale a ratio, multiply or divide both parts by the same number.

What is a ratio?

A ratio compares two quantities, showing their relative sizes. It is written with a colon, such as 2:3, read as two to three. This tells you that for every two of the first quantity there are three of the second.

Ratios can be part-to-part (comparing two groups, like 2 parts water to 3 parts squash) or part-to-whole. The total number of parts, here 2 plus 3 equals 5, is useful when dividing a whole into a ratio.

How to simplify a ratio

Divide every part of the ratio by their greatest common factor

To simplify, find the largest number that divides evenly into all parts of the ratio, then divide each part by it. This gives the ratio in its simplest, easiest-to-read form, exactly like reducing a fraction.

A worked example

Suppose a class has 20 boys and 30 girls, and you want the ratio of boys to girls.

Write it as a ratio: 20:30.
Find the greatest common factor of 20 and 30, which is 10.
Divide both parts by 10: 20 divided by 10 is 2, and 30 divided by 10 is 3.
Simplified ratio: 2:3.

In plain English: there are 2 boys for every 3 girls. The simplified 2:3 carries the same information as 20:30 but is far clearer.

Ratios in the kitchen and beyond

Scaling ingredients is pure ratio work. Our recipe scaler calculator keeps proportions right when you change servings, and our percentage guide helps when you convert ratios to percentages.

Scaling a ratio up or down

To keep a ratio the same while changing the amounts, multiply or divide every part by the same number. This preserves the proportion.

For example, to scale 2:3 up so the first part is 10, you multiply by 5 (since 2 times 5 is 10), giving 10:15. The relationship is unchanged; there are still 2 of the first for every 3 of the second. This is exactly how recipe scaling and mixing instructions work.

Ratios, fractions, and percentages

A ratio links neatly to fractions and percentages. In the ratio 2:3, the total is 5 parts, so the first quantity is 2/5 of the whole and the second is 3/5. Converting 2/5 to a percentage gives 40%, and 3/5 gives 60%. This is handy when you need to express a ratio as a share, such as how profits or a bill are split.

Frequently asked questions

How do I calculate a ratio?

Write the two quantities separated by a colon, then simplify by dividing both by their greatest common factor. For 20 boys and 30 girls, the ratio is 20:30, and dividing both by 10 gives 2:3. The simplified ratio means 2 boys for every 3 girls, expressing the same relationship in the clearest form.

How do I simplify a ratio?

Find the largest number that divides evenly into all parts of the ratio, called the greatest common factor, then divide each part by it. For 20:30, the greatest common factor is 10, so dividing both parts gives 2:3. Simplifying a ratio works just like reducing a fraction to its lowest terms.

How do I scale a ratio?

Multiply or divide every part of the ratio by the same number to keep the proportion. To scale 2:3 so the first part becomes 10, multiply both by 5, giving 10:15. The relationship stays identical. This is the method behind scaling recipes, mixing solutions, and adjusting quantities while keeping the balance right.

How do I convert a ratio to a percentage?

Add the parts to find the total, then express each part as a fraction of the total and convert to a percentage. In 2:3, the total is 5, so the first part is 2/5, which is 40%, and the second is 3/5, or 60%. This shows each part’s share of the whole.

What is the difference between a ratio and a fraction?

A ratio compares quantities to each other, like 2:3 comparing two groups. A fraction expresses a part of a whole, like 2/5. They are related: in the ratio 2:3, the first quantity is 2/5 of the total. Ratios are often part-to-part, while fractions are part-to-whole, though you can convert between them.

The bottom line

To calculate a ratio, write the quantities with a colon and simplify by dividing by their greatest common factor, so 20:30 becomes 2:3. Scale a ratio by multiplying or dividing every part by the same number, and convert it to a percentage by comparing each part to the total. Ratios power everything from recipes to bill splitting. For proportional scaling, try our recipe scaler calculator.