How to Use the Percentage Difference Calculator?

The procedure to use the percentage difference calculator is as follows:

Step 1: Enter two values in the respective input field.
Step 2: Now click the button “Calculate Percentage Difference” to get the result.
Step 3: Finally, the percentage difference for the given product will be displayed in the output field.

What Is Meant by Percentage Difference?

In mathematics, the percentage difference can be calculated by taking the difference between two values which is divided by the average of two values, and it is shown in percentage. The procedure to calculate the percentage difference is given as follows:

Take the difference between the two values.
Find the average of two values.
Divide the difference value by the average value.
Multiply the obtained solution by 100 to get the percentage (%).

For example, 20 and 30 are the values, the percentage decrease can be calculated as:

Step 1: 30 – 20 = 10

Step 2: (30 + 20)/2 = 25

Step 3: (10/25) x 100 = 40%

Hence, the percentage difference is 40, i.e. 40%.

Example

Calculating Percentage Difference

Percentage difference is a way to express the difference between two values as a percentage of their average. It is useful for comparing how much two values have changed or differ in relative terms.

The general approach to calculating percentage difference includes:

Finding the difference between the two values.
Calculating the average of the two values.
Dividing the difference by the average.
Multiplying the result by 100 to convert it into a percentage.

Calculating the Percentage Difference Between Two Numbers

The percentage difference between two values is calculated by the following formula:

\[ \text{Percentage Difference} = \frac{| \text{Value 2} - \text{Value 1} |}{\frac{\text{Value 1} + \text{Value 2}}{2}} \times 100 \]

Example:

If the two values are 50 and 70, the calculation is:

Step 1: Find the difference between the values: $ |70 - 50| = 20 $.
Step 2: Find the average of the values: $ \frac{50 + 70}{2} = 60 $.
Step 3: Divide the difference by the average: $ \frac{20}{60} = 0.3333 $.
Step 4: Multiply by 100 to get the percentage: $ 0.3333 \times 100 = 33.33\% $.

Calculating Percentage Increase

Percentage increase is a special case where the second value is greater than the first value. It is often used to calculate growth or improvement in a value.

Example:

If the two values are 100 and 120, the calculation is:

Step 1: Find the difference between the values: $ 120 - 100 = 20 $.
Step 2: Divide the difference by the original value (100): $ \frac{20}{100} = 0.2 $.
Step 3: Multiply by 100 to get the percentage: $ 0.2 \times 100 = 20\% $.

Calculating Percentage Decrease

Percentage decrease is used when the second value is smaller than the first value, indicating a loss or reduction.

Example:

If the two values are 80 and 60, the calculation is:

Step 1: Find the difference between the values: $ 80 - 60 = 20 $.
Step 2: Divide the difference by the original value (80): $ \frac{20}{80} = 0.25 $.
Step 3: Multiply by 100 to get the percentage: $ 0.25 \times 100 = 25\% $.

Real-life Applications of Calculating Percentage Difference

Calculating percentage difference has many practical uses, such as:

Comparing the prices of products to determine cost differences.
Tracking changes in performance metrics over time.
Measuring the difference in growth rates between two companies or economies.

Common Operations with Percentage Difference

Percentage Difference Formula: \[ \text{Percentage Difference} = \frac{| \text{Value 2} - \text{Value 1} |}{\frac{\text{Value 1} + \text{Value 2}}{2}} \times 100 \]

Percentage Increase: Used when the second value is larger than the first.

Percentage Decrease: Used when the second value is smaller than the first.

Calculating Percentage Difference Examples Table
Problem Type	Description	Steps to Solve	Example
Percentage Difference Between Two Numbers	Finding the percentage difference between two numbers.	Subtract the final value from the initial value. Take the absolute value of the result. Divide the result by the initial value. Multiply by 100 to get the percentage difference.	For the numbers 50 and 70, the difference is $ \|70 - 50\| = 20 $. Then, divide by the initial value 50, $ \frac{20}{50} = 0.4 $, and multiply by 100 to get $ 40\% $.
Percentage Increase	Finding the percentage increase between two numbers.	Subtract the initial value from the final value. Divide the result by the initial value. Multiply by 100 to get the percentage increase.	For the numbers 100 and 120, subtract 100 from 120 to get 20. Then, divide by 100, $ \frac{20}{100} = 0.2 $, and multiply by 100 to get a $ 20\% $ increase.
Percentage Decrease	Finding the percentage decrease between two numbers.	Subtract the final value from the initial value. Take the absolute value of the result. Divide the result by the initial value. Multiply by 100 to get the percentage decrease.	For the numbers 80 and 60, the difference is $ \|80 - 60\| = 20 $. Then, divide by the initial value 80, $ \frac{20}{80} = 0.25 $, and multiply by 100 to get a $ 25\% $ decrease.
Real-life Applications	Applying percentage difference to practical problems.	To calculate the percentage difference in prices between two products. To find the percentage difference in performance metrics over time.	If a product costs $100 one day and $120 the next, the percentage difference is calculated by $ \|120 - 100\| = 20 $, $ \frac{20}{100} = 0.2 $, and multiply by 100 to get a $ 20\% $ increase in price.