Percents & the Percent Formula: Definition & Examples

Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

Understanding percents can help you quickly determine how much things cost and many other things. In this lesson, you will learn what percents are and how to use the percent formula.

What is a Percent?

I went to the store yesterday and saw a shirt I really liked. The tag said it cost \$37.99, but it was currently on sale for 30% off. I only had \$30 with me. Was that enough to purchase the shirt or not? What exactly does a percent represent and how can we use it to calculate the cost of my new shirt?

The word percent comes from the Latin words per centum which means by the hundred, so a percent tells you how many parts you have out of 100 total. For example, if you had a bag full of 100 different colored marbles and I told you that 25% of the marbles in the bag were red, then you would know that exactly 25 of the marbles were red. Similarly, if my shirt cost exactly \$100, I would know that 30% of \$100 was \$30, so the shirt would cost \$70 (\$100-\$30 = \$70).

Percents can also be written as fractions or decimals. To convert a percent to a fraction, simply divide it by 100. That means that 30% could be written as 30/100 or 3/10. This could also be written as a decimal (3/10 = 0.3).

Percents are really easy to calculate when you have exactly 100 things, but it's rare for the amount of something to be exactly 100. Percents are still really useful though, and we can use the percent formula to calculate percents of any amount!

How to Use the Percent Formula

To find a percent of any number, you can use the percent formula where:

Part = the part of the whole

Whole = the total amount that the percent is operating on - also known as the base

Percent (%) = the number of parts per 100 - also known as the rate

Let's look at three different examples of how you could use the percent formula.

1. Find the part that is a percent of the whole

First, we will look at how to find the part that is a percentage of a whole amount. This is exactly what I needed to do when I wanted to know if I could buy the new shirt. I knew the total amount (the total cost of the shirt - \$37.99) and the percent (30%), and needed to find 30% of the whole so I would know how much the shirt would actually cost. To do this, we can cross multiply and solve for the part:

We could round this to \$11.40 since you can't pay part of a cent. So, how much will the shirt cost then? If the original price was \$37.99 and it is 30% off, we can subtract the part we just found from \$37.99 to find the new price:

\$37.99 - \$11.40 = \$26.59

So, I would have enough money to buy the shirt!

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