Ratio vs Percentage
Enter two numbers to see the same relationship as a simplified ratio and as percentages of the total. Understand how ratios and percentages convert into each other.
What Is the Ratio vs Percentage?
Ratios and percentages both describe how two quantities relate to each other, but they say it in different ways. A ratio compares the numbers directly, like 3:2, meaning three of one thing for every two of another. A percentage compares each part to the whole, like 60% and 40%. The same pair of numbers can be written either way. The ratio 3:2 converts to percentages of the total because the first part is 3 out of 5, or 60%, and the second is 2 out of 5, or 40%. Choosing which form to use depends on what you are comparing: a ratio is useful when the two amounts stand alone, while a percentage is useful when the total matters.
The Formula
For two numbers A and B, the simplified ratio is A:G : B:G where G is the greatest common divisor of A and B. Each part as a percentage of the total is (A / (A + B)) x 100 and (B / (A + B)) x 100. Each part as a percentage of the other is (A / B) x 100 and (B / A) x 100.
Example
A class has 18 boys and 12 girls. The ratio of boys to girls is 18:12, which simplifies to 3:2 by dividing both sides by 6. As a percentage of the class, boys make up 18 divided by 30 times 100, or 60%, and girls make up 12 divided by 30 times 100, or 40%. The same relationship reads as 3:2 as a ratio and as 60:40 as percentages.
Common Uses
Classroom math, comparing survey results, recipe scaling, mixture problems, checking homework, and understanding how financial ratios like debt to income relate to percentages.