Ratio Calculator
Divide both sides of the ratio by their greatest common factor.
Enter the two parts of the ratio
Enter the values in the same order as the problem states them. A ratio of boys to girls is not the same as girls to boys. Labels matter because the numbers describe a relationship, not just two values.
Use this tool to simplify ratios, compare quantities or scale a relationship. If the problem has three known values and one missing value, a proportion calculator may fit better.
What the simplified ratio tells you
A simplified ratio keeps the same relationship with smaller numbers. A ratio of 20 to 10 simplifies to 2 to 1. That does not mean the original counts were 2 and 1. It means the relationship is the same.
Ratios can be written with a colon, words or fraction style. For example, 2:1, 2 to 1 and 2/1 can describe the same relationship. The labels tell you how to read it.
A ratio is not always part of a whole. If the ratio is red to blue, the total may include both colors, but the ratio itself compares the two labeled groups.
The GCF step behind the answer
To simplify a two part ratio, divide both values by their greatest common factor. If the values are 20 and 10, the greatest common factor is 10. Divide both by 10 to get 2:1.
For ratios with more than two parts, divide every part by the common factor shared by all parts. If no common factor is shared, the ratio is already simplified.
Simplifying 24 to 36
If a class has 12 boys and 18 girls, the ratio of boys to girls is 12:18. The greatest common factor is 6. Divide both sides by 6 to get 2:3.
That answer means for every 2 boys, there are 3 girls in the same relationship. It does not mean the class has only 5 students.
Ratios are not always fractions
The biggest mistake is reversing the order. If the question asks for red to blue, keep red first. Reversing the ratio changes the meaning.
Another mistake is simplifying only one side. Whatever you do to one part of the ratio must be done to every part. Ratios preserve relationships by changing all parts together.
Ratio Calculator FAQ
How do I simplify a ratio?
Find the greatest common factor of the numbers in the ratio. Divide each part by that factor. For 20:10, the greatest common factor is 10, so the simplified ratio is 2:1.
For three part ratios, divide all three parts by the same common factor.
Does the order of a ratio matter?
Yes. A ratio compares labeled quantities in a specific order. Boys to girls is different from girls to boys. The numbers may be the same, but the meaning is reversed.
Always keep the order used by the question unless you intentionally want the opposite comparison.
Is a ratio the same as a fraction?
A ratio can be written like a fraction, but it often compares two labeled quantities. A fraction usually describes part of a whole.
For example, 2 boys to 3 girls is a ratio. The fraction of students who are boys would be 2 out of 5.
This distinction helps avoid a common mistake. The ratio 2:3 does not mean two fifths unless you are converting it into a share of the total.
Can a ratio have decimals?
Yes, but ratios are often easier to read as whole numbers. If the ratio has decimals, multiply every part by the same power of 10 to clear the decimals, then simplify.
For example, 1.5:3 can become 15:30, then simplify to 1:2.
When should I use a proportion instead?
Use a proportion when two ratios are set equal and one value is missing. A ratio calculator simplifies or compares a relationship. A proportion calculator solves for the missing value.
If your problem says something like 2:3 equals x:12, use a proportion.