Percents are a way of showing how two numbers compare to each other-- this can be useful when working with statistics or showing how much a total has changed over time. You can convert any number to a percent by expressing it as a portion of another number. You can do these calculations manually or with a calculator.
What Is It a Percent Of?
To calculate a percent of a number, you need to know which numbers you are comparing. A percent designates how much of one number is made up by another number, and is always calculated in relation to 100.
Say you have 100 sheep, and you want to figure out how many of them are sheared. If 0 out of 100 sheep are sheared, then 0 percent of the sheep are sheared. If all 100 of the sheep are sheared, then 100 percent of the sheep are sheared. If half, 50, of the sheep are sheared, then 50 percent of the sheep are sheared.
Percentage Through Division
You don't need a total to be 100 to figure out what percentage one number is of another. All you need is the total number and the number of the subset. To convert these numbers to a percent, divide the subset by the total, and multiply by 100.
For instance, say you have 72 books and 18 of them have green covers. To figure out what percent of the books have green covers, divide the number of green covers by the total number of books: 18 divided by 72 is 0.25. Multiply 0.25 by 100 to get the percent of green books:
0.25 x 100 = 25 percent
So, 25 percent of your books have green covers.
Using a Percent to Find a Total
You can also use this relation to find an amount represented by a percentage. To do this, convert the percent to a decimal, and multiply this by the number. You can convert a percent to a decimal by dividing it by 100. For instance, 19 percent is equal to 0.19. Multiply the decimal by an amount to find that percentage of the amount.
For instance, say you know that 70 percent of people in your town own cars. Your town has 15,000 residents. To find how many people own cars, convert 70 percent to a decimal and multiply it by 15,000. The decimal form of 70 is 70 divided by 100, or 0.7, so to find the number of people, multiply 0.7 by 15,000:
0.7 x 15,000 = 10,500
So, 10,500 people in your town own cars.
Percents Greater than 100
You can also have percentages that are greater 100 percent. A percentage larger than 100 shows that the number you are comparing to a total is larger than that total. This can be useful if you're comparing two different totals or showing a large increase in a number.
Farmer Bob has 24 cows, and Farmer Tom has 38 cows. To calculate Farmer Tom's cows as a percentage of Farmer Bob's cows, you'd follow the same procedure as with a smaller number. First divide 38 by 24, then multiply by 100:
38/24 = 1.5833 1.583 x 100 = 158.33 percent
So, Farmer Tom has 158.33 percent as many cows as Farmer Bob.
Percents can also be used to show how much a total has changed over time. This is called percentage change. To calculate percentage change, you'll need the original amount of a total and the amount of the total after it has changed. You first calculate the amount of change by subtracting the original total from the final total. Then divide the amount of change by original total and multiply by 100 to get the percentage. Percentage change can be shown by the following equation, where To is the original total and Tf is the final total. The same formula can be used regardless of whether the original total is larger than the final.
(Tf-To)/To x 100 = percentage change
Say Mary had $557.00 in her bank account at the beginning of the month, and $415.00 in her bank account at the end of the month. First, subtract the original total from the final:
415 - 557 = -142
Then divide by the original total, and multiply by 100:
-142/557 = -0.255 -0.255 x 100 = -25.5%
Because the percent change is negative, it shows that the percent change is a decrease--if the percent change is positive, the percent change is an increase. So Mary's bank account has decreased by 25.5 percent.