The percent difference is a mathematical way of comparing two independent quantities that use the same measurement, the way you may compare the number of candies in two separate bags or the height of two similar objects. The purpose is to find out by what percentage the two measurements differ. To do this, you need to find the difference in measurements, the average of the measurements, and then calculate the percent. If you are using a calculator, you input the data manually on your computer, apply the formula and calculate.

## Find the Difference of the Two Numbers

**In math, difference refers to subtraction.** To find the difference, subtract one quantity from the other. For example, if you had two bags of candies, and one had 18 candies and the other bag only had 16 candies, you subtract 16 from 18 to find the difference between the two bags.

*18 candies - 16 candies = 2 candies*

So, the difference between the two bags of candies is 2.

## Find the Average of the Two Numbers

**The average of two numbers is the quantity that exists halfway between them,** such as how the number 3 exists between the numbers 2 and 4, but on a larger scale. Calculating the average of two numbers is simple. You add the two together to find their total sum and then you divide that sum by 2.

Using the previous example, the two bags contained 16 and 18 candies individually. To find the total number of candies in the two bags, you add the two bags together.

*16 + 18 = 34*

Once you have the total number, you divide that total by 2 to find the average of the two bags.

*34 / 2 = 17*

This means the average of number of candies is 17.

## Find the Percent Difference

**The percent difference between two numbers is the difference of the two numbers divided by their average.** Looking at the previous examples, you know that the difference between the two bags of candies is 2 and the average of the two bags is 17. When you divide the two, you get a decimal. This is the percent difference.

*2 / 17 = 0.1176*

Once you have the decimal, you convert it to a percentage. To do this, you multiply it by 100. Or, you move the decimal point two spaces to the right.

So,

*0.1176 x 100 = 11.76 percent*

This means that the percent difference between the bag of 16 candies and the bag of 18 candies is 11.76 percent.

## More Examples

**If one boy stands 63 inches tall and another stands 67 inches tall,** what is the percent difference between their heights?

The difference between the two heights is *67 inches - 63 inches = 4 inches*

The average of the values is *(67 + 63) / 2 = 65 inches*

The percent difference between the two heights is *100 x (4 / 65) = 6.15* percent

Another example:

If gas costs $2.14 at one station and $2.29 at another, what is the percent difference between the two prices?

The difference between the two gas prices is *$2.29 - $2.14 = $.15 cents*

The average of the two prices is *(2.29 + 2.14) / 2 = 2.215 cents*

The percent difference is *100 x (.15 / 2.215) = 6.77 percent*