Percent Difference - Definition, Examples, How To Calculate?

Percent Difference

The percentage difference of any two numbers is the 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. Let us learn more about the percent difference in this article.

1.	What is Percent Difference?
2.	Percent Difference between Two Numbers
3.	How to Calculate Percentage Difference?
4.	Percentage Difference vs Percentage Change
5.	FAQs on Percent Difference

What is Percent Difference?

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 defined as 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 percent difference between two numbers and the steps to calculate the same.

Percent Difference between Two Numbers

The percentage difference between two numbers is the method to calculate the difference between any two values in terms of the percentage of the average of both the values. It is used when the quantities are of the same kind, for example, numbers of cars sold in January and February, heights of Ron and Harry, the weight of two objects, etc. While calculating the percent difference between two numbers, we take the average value of both as a reference value. The average is calculated by dividing the sum of both numbers by the total number of quantities taken. Let us find the percentage difference of 10 and 32.

Difference of 10 and 32 = 32 - 10 = 22

Average of 10 and 32 = (10 + 32)/2 = 42/2 = 21

Percent difference = 22/21 × 100 = 104.76%

How to Calculate Percentage Difference?

The calculation of the 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 = 65 and b = 35.

1. Find the difference between two numbers, i.e, a - b = 65 - 35 = 30.
2. Find the average of two numbers, i.e (a + b)/2 = (65 + 35)/2 = 100/2 = 50.
3. Take the ratio of the difference and the average, (a-b)/((a+b)/2) = 30/50 = 3/5.
4. 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 percentage difference of any two numbers is the absolute value of the ratio of their difference and their average multiplied by 100. The percentage difference formula or the percent difference equation of two numbers a and b is:

\(\left| \dfrac{a-b}{ \left(\dfrac{a+b}{2} \right)} \right| \times 100\%\)

Using this formula, we can determine the difference in percentage between any two values.

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 ratio 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 vice-versa.
While calculating the percentage difference, 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 the value is taken 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.

► Related Topics

Listed below are a few related topics to the concept of percentage difference in math.

• Percent Difference Calculator
• Percentage Increase Calculator
• Percent Proportion