How to Calculate Percent Difference – Definition, Formula, Examples

What Is the Percent Difference in Math?

Percent difference is the ratio of the absolute difference between two values to the average of the two values, calculated as a percentage. 

Percent Difference $= \frac{Absolute \; Difference}{Average} \times 100$ 

In simple words, the percent difference is the percentage of the relative difference. The relative difference between two quantities compares the difference between the two values in relation to their average. 

Relative Difference $= \frac{Absolute \; Difference}{Average}$

The percent difference is frequently used when comparing data sets or estimating the degree of change between two numbers.

What Is the Percent Difference Formula?

The percentage difference is the ratio of the difference in their values to their average, multiplied by 100.

Percent difference formula for the two values A and B can be given as 

Percent difference $= \frac{A – B}{ \frac{(A + B)}{2}} \times 100$

How to Find Percent Difference

Follow the steps given below to learn how to calculate the percent difference between two values A and B.

Step 1: Find the absolute difference. 

Find the absolute value of the difference between A and B. The order does not matter since we will be taking the absolute value.

Absolute Difference $= |A \;-\; B|$

Step 2: Find the average of A and B. Simply add the values together and divide the sum by 2. 

Average $= \frac{(A + B)}{2}$

Step 3: Divide the absolute difference by the average and multiply by 100 in order to calculate the percent difference. 

Percent Difference $= \frac{Absolute \; Difference}{Average} \times 100$

Percent difference $= \frac{|A \;-\; B|}{ \frac{(A + B)}{2}} \times 100$

Percent Difference between Two Numbers

The percent difference between the two numbers is expressed as follows:

Percent Difference $= \frac{|A – B|}{ \frac{(A + B)}{2}} \times 100$

Example: Alex has 10 years of working experience. Paxton has 20 years of working experience. What is the percent difference?

Here, $A = 10, B = 20$

Note that these values represent the working experience of Alex and Paxton in years.

Can you decide which value is more important here? No, both values hold the same importance!

In such cases, we can use the percent difference formula. 

We choose the average value as the reference point. We take absolute difference to treat both values equally. So, the order does not matter when you subtract.

$|A \;-\; B| = |10 \;-\; 20| = | \;-\;10| = 10$

$\frac{(A + B)}{2} = \frac{10 + 20}{2} = 15$

Percent Difference $= \frac{|A – B|}{\frac{(A + B)}{2}} \times 100$

Percent Difference $= \frac{10}{15} \times 100$

Percent Difference $≈ 66.67\%$

Percent Difference vs. Percent Change

Percent Difference	Percent Change
Percent Difference $= \frac{|A – B|}{\frac{(A + B)}{2}}100$	Percent Change $= \frac{(Final \;Value\; -\; Initial \;Value)}{Initial \;Value} \times 100$
It is calculated by taking the absolute difference between the two values, dividing it by the average of the two values, and multiplying by 100.	It is calculated by taking the absolute change, dividing it by the initial value, and multiplying by 100.
Reference point is the average of two values.	Reference point is the initial value.
We ignore the minus sign as we take the absolute value of the difference.	If the value is positive, it means there is an increase. If the value comes out to be negative, it indicates a decrease.

Facts about Percent Difference

Conclusion

You know the percent difference, definition, concept, formula, etc. Let’s move toward the numerical section of a percent difference, including solved examples and MCQs, for a clearer understanding.

Solved Examples on Percent Difference

1. Mr. Dunphy’s garden has 78 rose plants. Mr. Prichet’s garden has 106 rose plants. Find the percent difference.

Solution: 

Firstly, we will calculate the difference between the two numbers.

Difference $= 78\;-\;106 = \;-\; 28$

We can remove the negative sign by giving the absolute value of the difference.

Absolute Difference $= |Difference| = |\;-\;28| = 28$

Average $= \frac{78 + 106}{2} = \frac{184}{2} = 92$

Now, find the percentage difference.

Percentage Difference $= (\frac{Absolute \;Difference}{Average}) \times 100$

Percentage Difference $= \frac{28}{92} \times 100$

Percentage Difference $≈ 30.43\%$

2. In a video game tournament, Team A scored 980 and Team B scored 1220 points. What is the percentage difference between the scores?

Solution:

On calculating the difference between the two scores, we get

Difference $=$ Score of Team B – Score of Team A $= 1220\;-\;980 = 240$

Absolute difference $= | 240 | = 240$

Average $= \frac{1220 + 980}{2} = 1100$

Now, we can calculate the percentage difference between the teams’ scores.

Percentage Difference $= (\frac{Difference}{Average})\times100$

Percentage Difference $= (\frac{240}{1100}) \times 100$

Percentage Difference $≈ 21.81\%$

3. What is the percentage difference between 7.2 and 8.5?

Solution:

Here, we have to calculate the difference between two numbers.

Difference $= 7.2 \;-\; 8.5 = \;-\; 1.3$

We will remove the negative sign by taking the absolute value of the difference.

Absolute Difference $= |Difference| = |\;-\;1.3| = 1.3$

Now, you can calculate the percentage difference.

Average $= \frac{7.2 + 8.5}{2} = 7.85$

Percentage Difference $= (\frac{Absolute \;Difference}{Average}) \times 100$

Percentage Difference $= (\frac{1.3}{7.85}) \times 100$

Percentage Difference $≈ 16.56\%$

Practice Problems on Percent Difference

Frequently Asked Questions on Percent Difference