how to find percent difference

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 percentage difference.

1.	Percentage Difference Definition
2.	How to Calculate Percent Difference?
3.	Percentage Difference Formula
4.	Percentage Difference vs Percentage Change
5.	FAQs on 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 = 65 and b = 35.

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

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

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

d) 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.

Percent Difference Formula

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 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 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 percentage difference.

Ratio
Unitary Method
Decimal
Denominator
Numerator
Percentage
Percentage Calculator
Percentage Change
Percent to Fraction Calculator
Percentage Increase Calculator
Decimal to Percent Calculator

Percentage Difference Examples

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

\(
\left| \dfrac{a-b}{ \left(\dfrac{a+b}{2} \right)} \right|\times 100\%\\[0.2cm]
=\left| \dfrac{30-50}{ \left(\dfrac{30+50}{2} \right)}\right| \times 100\%\\[0.2cm]
= \left|\dfrac{-20}{ 40} \right| \times 100\%\\[0.2cm]
=50\%
\)

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 percentage difference is calculated using the formula of percent difference:

\(\left| \dfrac{a-b}{ \left(\dfrac{a+b}{2} \right)} \right|\times 100\%\\[0.2cm]
=\left| \dfrac{35-53}{ \left(\dfrac{35+53}{2} \right)}\right| \times 100\%\\[0.2cm]
= \left|\dfrac{-18}{ 44} \right| \times 100\%\\[0.2cm]
\approx 41\%\)

Answer: The percentage difference = 41%.

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Practice Questions on Percentage Difference

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FAQs on Percentage Difference

Does the Percentage 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 Percentage Difference in Chemistry?

The percentage difference formula or the percent difference equation of two numbers a and b is \(\begin{align}\left|\dfrac{a-b}{ \left(\dfrac{a+b}{2} \right)} \right| \times 100\%\end{align}\). 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.

What is the Difference between Percentage Difference and Percentage 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 Percentage 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 Percentage 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

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%.