Percentage Change

The percentage change (or) the percentage change of a quantity is the ratio of the difference in the quantity to its initial value multiplied by 100. There is always a change in percentage change (or) the percent change of a quantity when the percent of its initial value is either increased or decreased to obtain its final value.

Percentage Change is the difference coming after subtracting the old value from the new value and then divide by the old value and the final answer will be multiplied by 100 to show it as a percentage. Generally, to convert a fraction into a percent, we multiply it by 100.

For example, 3/4 × 100 = 75%

In the same way, we multiply the fraction (ratio) of the difference in quantity to its initial value by 100 to get the percentage change. The percentage change gives the difference in quantity out of 100.

Understanding Percentage Change with help of an example.

Robert started a business with an initial investment of Rs. 30,000 and in one year, it grew to Rs. 70,000. The growth of Robert is 40000 (70000 - 30000). Michael started a business at the same time as Robert with an initial investment of Rs. 25,000 and in one year, it grew to Rs. 65,000. The growth of Robert is 40000 (65000 - 25000). Whose business grew rapidly?

We can say that the growth value of both businesses is 40000, but the growth rate is not the same.

The growth rate should always be calculated with respect to the initial value and only then the rates can be compared. The percent change gives the difference in a quantity with respect to its initial value. It gives the growth/decay rate. This helps us in comparing the quantities.

The formula for the percentage change is defined as the ratio of the difference of final value and initial value to the initial value. The formula of percentage change is mathematically expressed as:

There are two methods to calculate the percent change. One is using the above formula and the other is using proportions.

Let us apply both methods to solve the following example.

For example, If 64 is increased to 120, find the percent change.

To perform these methods, we need to identify the initial and final values.

• Initial Value = 64
• Final Value = 120

Method 1:

a)Subtract the initial value from the final value
Final Value - Initial Value =120 - 64 = 56

b) Divide this by the absolute value of the initial value
Final Value - Initial Value ÷ |Initial Value| = 56 ÷ |64| = 0.875

c) Multiply the result by 100
(Final Value - Initial Value) ÷ | Initial Value | × 100

= 0.875 × 100 = 87.5%

Since the answer is positive, it is a percent increase.

Percent Increase = 87.5%

Let's understand this process easily using the following image.

Method 2:

In this method, we assume that

• the initial value corresponds to 100%
• the final value corresponds to x%

Proportion = 64 / 100 = 120 / x

Solve for x by cross multiplication.

64x = 12000
x = 187.5%

This is the percent of the final value when compared to the initial value.

To find the percent change, we just subtract 100% from this.

Percent change = 187.5% - 100% = 87.5%

Since it is positive, it is a percent increase.

Percent Increase = 87.5%

Let's understand this process easily using the following image.

Important Notes

• The formula for percentage change is: [(Final Value - Initial Value) ÷ | Initial Value |] × 100
• If a quantity is increased by r%, then its final value is obtained by multiplying its initial value by 1 + r / 100
• If a quantity is decreased by r%, then its final value is obtained by multiplying its initial value by 1 - r / 100

☛Related Articles

Check the following pages to know more about the percentage change and its related topics.

• Percentages
• Proportion
• Percent Proportion

How Do You Find the Percentage Change?

The percentage of change is calculated using the formula: (Final Value - Initial Value) ÷ | Initial Value | × 100

Can You Calculate the Percentage Change of Percentages?

Yes, we just calculate it using the formula: (Final Percentage - Initial Percentage) ÷ | Initial Percentage | × 100

What is the Meaning of Percentage Change?

The percentage change (or) the percentage change of a quantity is the ratio of the change in the quantity to its initial value multiplied by 100.

How Do You Find the Percentage Change of Multiple Changes?

To find the percentage change of multiple changes we need to apply the percentage change formula multiple times as required. Final Value - Initial Value ÷ | Initial Value | × 100

What is the Percentage Change from 5 to 9?

To find the percentage change from 9 to 5 we will apply the percentage change formula: (Final Value - Initial Value) ÷ | Initial Value | × 100

• Initial Value = 5
• Final Value = 9

Final Value - Initial Value = 9 - 5 = 4

= (4 ÷ 5) × 100 % = 80%

What are the Two Types of Percentage Change?

Increase and decrease are the two types of percentage change, that are used to express the ratio of how an initial value or old value compares to the result of a change in a new value or final value.

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.