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# Percent Difference Formula

The percent difference formula finds the absolute value of the change in value. For any two numbers that belong to the same category, we calculate the absolute value of the ratio of their difference to their average multiplied by 100. Let’s learn to calculate and apply the percent difference formula.

## What is Percent Difference Formula?

The percentage difference formula calculates the difference between two numbers which is expressed in percentage. The percent difference is the ratio of the difference in their values to their average multiplied by 100. Since the order of the number doesn't matter we calculate the absolute difference between the two numbers. We calculate the average of the values as a reference value to avoid confusion between choosing the initial and final values at the denominator.

### Percentage Difference Formula

The percent difference formula for two values, a and b:

Percentage difference = |Absolute difference between the two values/ Average of both the values| × 100%

Percentage difference = \( \dfrac{\mid a-b \mid}{\dfrac{a+b}{2}} \times 100%\)

The percentage difference formula can also be used to calculate the difference between the initial and final values of any quantity after a change. Here, using the same above formula 'a' will represent the initial value while 'b' will represent the final value. We can understand the steps to find the percentage difference formula using the following flowchart.

## Examples Using Percent Difference Formula

**Example 1: **The height of a tower is increased from 30 ft to 50 ft. Find the percent difference using the percent difference formula.

**Solution:**

To find the percentage difference between the heights of the given tower.:

The initial height is, a = 30 ft. The final height is, b = 50 ft.

The percent difference is calculated using the formula of percent difference:

[|(50-30)|/(50+30)/2]× 100

= [20/40] ×100

= 50%

**Answer: **The percentage difference = 50%.

**Example 2: **Mia wrote 53 instead of writing 35. Find the percent difference between the numbers 35 and 53.

**Solution:**

To find the percent difference between the numbers 35 and 53:

The given two numbers are:

a = 35 and b = 53.

The percent difference is calculated using the formula of percent difference:

[|(35-53)|/(35+53)/2] ×100

=[|-18|/44]100

=40.9%

=41%

**Answer:** The percentage difference = 41%.

Example 3: Charles works 180 hours per month and Steve works 240 hours per month. Calculate the percentage difference.

Solution:

Let initial value = 180, Final value = 240

Applying the percentage difference formula,

The percentage difference = [Difference/average] × 100

=[|(180-240)|/(180+240)/2]× 100

= [|-60|/210]× 100

= 600/21

= 200/7

= 28.57 = 29%

**Answer:** The percentage difference = 29%

## FAQs on Percent Difference Formula

### How do we Apply the Percentage Difference Formula?

We calculate the percentage increase and decrease between two numbers while we are comparing them using the percentage difference formula. We consider one number as the initial value and the other as the final value. Find the difference between them and find the average of them. Difference/ Average is multiplied by 100.

### What Is The Difference in Percentage Between Two Numbers Using Percentage Difference Formula?

The difference in percentage between two numbers is the difference between them divided by their average multiplied by 100. The percentage difference formula can be given as, [|(a-b)|/(a+b)/2] × 100, where a and b are the two numbers.

### How to Find Percentage Difference between 5 to 2 Using Percentage Difference Formula?

The percentage change is the percentage difference and we use the percent difference formula:

= [|(a-b)|/(a+b)/2] × 100

= [|(5-2)|/(5+2)/2] × 100

=[3/3.5] × 100 = 85.7%

Thus 85.7% difference between 5 and 2.

### Is the Percentage Difference Formula the Same as the Percentage Change Formula?

No, both are different. The percentage difference formula gives the ratio of the difference between the two values to their average multiplied by 100. On the other hand, the percentage change formula gives the ratio of the difference between the two values to the initial value multiplied by 100. In Percentage difference, we calculate the difference in the percentage of the values, whereas, in percentage change, we calculate the percentage of the change of one value over the other relatively.

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