Percents and Ratios: How to Convert and Understand the Difference

Percents and ratios are among the most commonly used mathematical concepts in everyday life. They can be found everywhere: in statistics, retail sales, school grades, personal finances, and even recipes. However, many people still hesitate when they have to convert one to the other.

As we'll see in more detail later, a percentage is actually just a ratio expressed on a base of 100. Understanding this relation allows you to:

• Convert a ratio to a percentage;
• Get a ratio from a percentage;
• Calculate a percentage from a ratio; or even
• Determine the difference between a ratio and a percentage.

In this article, we will examine the relationship between percents and ratios using simple definitions, formulas, and step-by-step examples.

What is a percent?

A percentage expresses a proportion 🇺🇸. This proportion refers to a whole compared to one hundred parts. Therefore, a percentage, percent, or per cent is nothing more than a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign ($\%$), although the abbreviations $\text{pct.}$, $\text{pct}$, and sometimes $\text{pc}$ are also used. The concept of percentage is used in all sorts of contexts:

• Money matters (e.g., VAT, discounts, interest, losses, profits);
• Estimating the proportions of mixtures (e.g., % alcohol in wine);
• Quantifying progress (e.g., 200% increase, 10% decrease);
• Indicating the slope of a road;
• Giving the grades of tests and exams;
• Compiling statistics; or
• Making advertising offers (e.g., 50% free).

To learn more about it, check our percentage calculator 🇺🇸!

What is a ratio?

A ratio is a relationship between two quantities of the same type. It may be specified either by giving both constituting numbers, written as $\text{a to b}$ or $\text{a:b}$, or by giving just the value of their quotient ⁠$\text{a/b}$. Equal quotients correspond to equal ratios. The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or measurements of lengths, weights, time, etc. In most contexts, both numbers are restricted to be positive. A ratio can also extend to several numbers (e.g., $2\!:3\!:7$).

We also have a ratio calculator 🇺🇸 to help you with your ratio calculations.

A percentage is a ratio expressed as a fraction of 100, while a ratio is a more general comparison between two quantities. Percentages are often used to describe proportions or variations in quantities, while ratios are used to describe the relationship between different quantities.

For example, a ratio of $1\!:\!4$ means:

So, when you convert a ratio or fraction to a percentage 🇺🇸, you express the same relationship using 100 as the reference point.

A formula for converting the ratio to a percentage can be applied directly to any value to obtain the required percentage. The formula is as follows:

It is expressed using the percentage symbol ($\%$).

Example

Let's say you have a ratio of $3\!:\!8$. Here's a quick step-by-step guide to convert it to a percentage easily:

1. Divide the first number in the ratio by the second number.

2. Multiply the result by 100.
3. Finally, add the percent symbol (%).

To find the percent of a ratio is pretty straightforward because when a quantity is split according to a ratio, each "part" represents a share of the whole. To turn those parts into percentages:

1. Add the parts of the ratio to get the total number of parts.
2. Divide each part by the total to get its fraction of the whole.
3. Convert to a percent by multiplying by 100.

Example

Suppose you have a ratio of 2:3:5 (total = 10 parts):

If you know percentages, you can convert them into a ratio by:

1. Writing them as whole numbers (remove the % sign).
2. Putting them in comparison form.
3. Simplifying if needed.

For example, let's say you have 60% men and 40% women in a group. You can write it as:

Percents and ratios are so intricately woven that they can easily be confused. So, we've created an easy-to-read table that sums up their differences and makes their comparison clearer.

Percents and ratios are closely related. Indeed, a percentage is just a ratio with a denominator of 100. Knowing how to convert a ratio to a percentage (and vice versa) makes it easier to compare data, understand statistics, and work with proportions in all areas.