Ratio To Percentage Calculator

What this calculator does

So, you have a ratio and you want it expressed as a percentage. This tool does that. Enter the two parts of the ratio and it returns the first part as a percentage of the second.

You type the two numbers of the ratio, and the tool gives back a single percentage figure.

How to use it

1. Enter the first part of the ratio.
2. Enter the second part of the ratio.
3. Press Calculate.

Neither part should be zero, since the second part is what the first is measured against.

Turning a ratio into a percent

A percentage is just a way of expressing a ratio using 100 as the reference. To convert a ratio to a percentage, you divide the first part by the second and multiply by 100. That is exactly what the tool does: for the ratio 3 to 2, it works out 3 divided by 2, which is 1.5, then multiplies by 100 to give 150 percent. Multiplying by 100 rescales the comparison so it is measured out of a hundred, which is what "percent," meaning per hundred, literally asks for.

What the percentage means here

The result tells you how big the first part is relative to the second, as a percentage. A ratio of 1 to 4 gives 25 percent, meaning the first part is a quarter of the second. A ratio of 1 to 1 gives 100 percent, since the two parts are equal. Reading it this way is often more intuitive than a raw ratio: saying one quantity is 25 percent of another lands more clearly than saying they are in the ratio 1 to 4, even though both say the same thing.

When the percentage is over 100

If the first part is bigger than the second, the percentage comes out above 100, and that is perfectly correct. The ratio 3 to 2 gives 150 percent because the first part is one and a half times the second. Percentages over 100 simply mean the first quantity exceeds the one it is compared against. This is the same reason an investment that grows to more than its starting value is described as, say, 173 percent of what it was. A figure above 100 percent is a normal and meaningful result, not a mistake.

A worked example

Enter a ratio of 3 to 2. The tool divides 3 by 2 to get 1.5, then multiplies by 100 to give 150 percent. Enter 1 to 4 instead, and it divides 1 by 4 to get 0.25, then multiplies by 100 for 25 percent. So the first part is a quarter of the second.

Questions people ask

How is a ratio converted to a percentage?

Divide the first part by the second and multiply by 100. The ratio 3 to 2 becomes 150 percent.

What does the percentage represent?

How large the first part is relative to the second. A ratio of 1 to 4 is 25 percent, so the first part is a quarter of the second.

Can the percentage be more than 100?

Yes. When the first part is larger than the second, the result is above 100 percent, which just means it exceeds the second part.

Why can't the second part be zero?

Because it is the amount the first is compared against, and dividing by zero has no meaning.

What if I want a fraction instead?

The ratio to fraction calculator writes the ratio as a fraction or mixed number rather than a percentage.

References

On expressing a ratio as a percentage. A ratio is converted to a percentage by dividing and multiplying by 100.

1. Eric W. Weisstein, "Percent," from MathWorld, a Wolfram resource, on converting a ratio or fraction to a percentage by multiplying by 100.
2. Eric W. Weisstein, "Ratio," from MathWorld, a Wolfram resource, on the ratio of two numbers.