Percent Difference Formula

Introduction to Percent Difference Formula

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.

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.

Find the difference between two numbers, i.e, a – b = 65 – 35 = 30.

Find the average of two numbers, i.e (a + b)/2 = (65 + 35)/2 = 100/2 = 50.

Take the ratio of the difference and the average, (a-b)/((a+b)/2) = 30/50 = 3/5.

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:

[{(a − b)}/{(a + b)/2}] × 100 %

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

Solved Examples on Percentage Difference Formula

Example 1: The height of a tower is increased from 30 ft to 50 ft. Find the percentage difference.

Solution:

Let the initial height be a = 30 ft. and the final height be, b = 50 ft.

So, difference = b – a = 50 – 30 = 20 ft.

Average = (b + a)/2 = (50 + 30)/2 = 80/2 = 40 ft.

The percent difference is calculated using the formula:

(Difference/Average) × 100%

= 20/40 × 100%

= 50%

The percentage difference between the values of height of the tower is 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.

Here, b – a = 53 – 35 = 18

and, (b + a)/2 = (53 + 35)/2 = 88/2 = 44.

The percentage difference is calculated using the formula:

(Difference/Average) × 100%

= 18/44 × 100%

= 40.9%

The percent difference between 35 and 53 is of 41% approximately.

Example 3: If the price of two pairs of shoes at a store is 120 and 70 respectively, find the percent difference between the two prices.

Solution:

Let the prices be a = 120 and b = 70.

So, difference = a – b = 120 – 70 = 50.

Average = (a + b)/2 = (120 + 70)/2 = 190/2 = 95.

The percent difference is calculated using the formula:

(Difference/Average) × 100%

= 50/95 × 100%

= 52.63 %

The percentage difference = 52.63 %.

Frequently Asked Questions on Percentage Difference Formula

1: What is the Percentage Difference?

Answer: The percentage difference is defined as the ratio of the difference between two numbers to their average expressed in the form of a percentage. It is a way to express the difference between two quantities of the same kind. It is calculated by using the formula: |Difference/Average| × 100%.

2: What is the Percent Difference between the Two Results?

Answer: The percent difference between the two results say a and b is calculated as |(a – b)/(a+b)/2| × 100%. In simple words, it is the ratio of the difference to the average of two numbers multiplied by 100.

3: What is Relative Percent Difference?

Answer: The relative percent difference is the difference in the percentage of the initial value and the final value. It is measured as the division of difference of values by the average of the initial and final values multiplied by 100.

4: How to Calculate Percent Difference between Two Numbers?

Answer: To calculate the percent difference between two numbers say a and b, we use the following formula: |(a – b)/(a+b)/2| × 100%. In other words, first, we find the difference between both numbers followed by finding the average of two numbers. At last, we multiply the ratio of the difference to average by 100 and simplify the result.

5: What does a Negative Percent Difference Mean?

Answer: If you get a negative value for percentage difference, then ignore the negative sign and write the absolute value as the final answer. While calculating the percent difference, we take the modulus or the absolute value of the final simplified value.

6: Does the Percentage Difference Indicate Accuracy and Precision?

Answer: Percent difference indicates accuracy and precision since it takes all the experimental values and compares them with each other.

7: What is the Difference between Percentage Difference and Percentage Change?

Answer: 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. It takes the average of two values as the reference.

8: What does Percent Difference Tell you about an Experiment?

Answer: The percent difference of any two numbers is the absolute value of the ratio of their difference and their average multiplied by 100. It tells us the difference between the two values with reference to their average in percent form.

9: What is the Difference between Percent Error and Percentage Difference?

Answer: 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/estimated value of the same quantity. Below are the formulas for both. Percent error is just the absolute value of the percent change.

If a is the expected value and b is the actual value observed, then,

Percent error = [|b-a|/|a|] × 100%.

The percent difference between two numbers a and b = (difference between a and b/average of a and b) × 100%.