Percent Difference
The percentage difference of any two numbers is the absolute value of the ratio of their difference and their average multiplied by 100. The word percent means the part of the number 100. It is a fraction or a ratio where the whole value is always 100. For example, the score of Jess is 70% which means Jess has scored 70 out of 100 in a particular subject. A percent can be calculated by using the unitary method and changing the denominator of the fraction to 100. Percent can be used in calculating not only the exact numbers out of 100 but also the difference between any two numbers by finding the percent difference.
Percentage Difference Definition
Percentage difference tells us the measurement of two different experimental values where one value is higher than the other value. In other words, the percentage difference is the absolute value of the ratio of the difference between two numbers and their average, expressed as a percentage. For example, if we need to find out the percentage of customers in April over the customers in May, the percent difference formula will be used. Let us look at the steps of calculating percentage difference to understand this better.
How to Calculate Percentage Difference?
The calculation of percentage difference of any two values a and b is easy if you follow the steps written below:
 Step 1: Find the difference between the two numbers, i.e a  b.
 Step 2: Then, find the average of two numbers, i.e (a+b)/2
 Step 3: Take the ratio of the difference and the average.
 Step 4: Multiply the fraction obtained by 100 and simplify your answer.
Let us see how to calculate the difference in percentage using an example.
Example: Calculate the percentage difference between the numbers 35 and 65
Let us first assume that a = 35 and b = 65
a) Find the difference between two numbers, i.e, a  b = 35  65 = 30
b) Find the average of two numbers, i.e (a + b)/2 = (35 + 65)/2 = 100/2 = 50
c) Take the ratio of the difference and the average, (ab)/((a+b)/2) = 30/50 = 3/5
d) Find its absolute value, i.e \(\left \dfrac{ab}{ \left(\dfrac{a+b}{2} \right)} \right = \left \dfrac{3}{5}\right=\dfrac{3}{5}\)
e) Multiply this by 100%, 3/5 × 100% = 60%
Thus, The percent difference = 60%
We can understand the steps to find the percentage difference of two numbers using the following flowchart.
Percentage Difference Formula
The percent difference of any two numbers is the absolute value of the ratio of their difference and their average multiplied by 100. The percent difference formula or the percent difference equation of two numbers a and b is:
\(\left \dfrac{ab}{ \left(\dfrac{a+b}{2} \right)} \right \times 100\%\)
Using this formula, we can determine the difference in percentage between any two values. The absolute value is taken as the difference in values no matter the order of the numbers.
Percentage Difference vs Percentage Change
Percentage difference and percentage change are two concepts that people often end up using interchangeably but they are different from each other. Listed below are a few differences between percentage difference and percentage change.
Percentage Difference  Percentage Change 

It is the percentage of the difference between two values and the average of two values where one value is higher or lower than the second value.  It is the difference between two values as a percentage of one or both values where the old value is compared to the new value or viceversa. 
While calculating the percentage, the difference between both values is divided by the average of the two values.  While calculating the percentage change, the difference between both values is divided by the old value. 
If the derived answer is negative, the minus sign has to be ignored and taken the value as it is.  If the derived answer is negative, the negative value shows a decrease whereas a positive value shows an increase in the value. 
Percent Difference Related Topics
Listed below are a few related topics to the concept of percent difference.
Solved Examples on Percent Difference

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:
Given that the initial height is, a = 30 ft. and the final height is, b = 50 ft. The percent difference is calculated using the formula of percent difference:
\(
\left \dfrac{ab}{ \left(\dfrac{a+b}{2} \right)} \right\times 100\%\\[0.2cm]
=\left \dfrac{3050}{ \left(\dfrac{30+50}{2} \right)}\right \times 100\%\\[0.2cm]
= \left\dfrac{20}{ 40} \right \times 100\%\\[0.2cm]
=50\%
\)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:
The given two numbers are a = 35 and b = 53. The percent difference is calculated using the formula of percent difference:
\(\left \dfrac{ab}{ \left(\dfrac{a+b}{2} \right)} \right\times 100\%\\[0.2cm]
=\left \dfrac{3553}{ \left(\dfrac{35+53}{2} \right)}\right \times 100\%\\[0.2cm]
= \left\dfrac{18}{ 44} \right \times 100\%\\[0.2cm]
\approx 41\%\)Answer: The percentage difference = 41%.
FAQs on Percent Difference
Does the Percent Difference Indicate Accuracy and Precision?
Percent difference indicates accuracy and precision since it takes all the experimental values and compares them with each other.
How do you Find the Percent Difference in Chemistry?
The percent difference formula or the percent difference equation of two numbers a and b is \(\begin{align}\left\dfrac{ab}{ \left(\dfrac{a+b}{2} \right)} \right \times 100\%\end{align}\). We use the percent difference formula in Chemistry to find the percentage difference between two experimental values. The percent difference formula in Physics is same as the above formula, where a and b are two experimental values.
How is a Quality Percentage Calculated?
The quality percentage (or) percent error is just the absolute value of the percent change. If a and b are the initial and final values respectively, then ((ba)/a) x 100%
What is the Difference between Percent Difference and Percent Change?
Percentage change gives the change in a quantity with respect to its initial value, expressed as a percentage. It gives the growth/decay rate. Percent difference indicates precision since it takes all the experimental values and compares them with each other.
What does the Percent Difference Between the Two Numbers Tell You?
The percent difference of any two numbers is the absolute value of the ratio of their difference and their average multiplied by 100.
What is the Difference between Percent Error and Percent Difference?
The percent difference is the absolute value of the difference between two values as a percent of the average of the two values. Whereas, percent error is calculated when one value is compared to the standard value of the same quantity. Below are the formulas for both. Percent error is just the absolute value of the percent change. If a and b are the initial and final values respectively, then
\(\begin{align}&\text{Percent Error} \\[0.2cm]&= \left(\!\dfrac{ ba}{a} \!\!\times\!\! 100 \!\!\right)\!\!\%\end{align} \)
The percent difference between two numbers a and b is,
\(\left \dfrac{ab}{ \left(\dfrac{a+b}{2} \right)} \right \times 100\%\)