Percentage Change Formula

Percentage Change Formula (Table of Contents)

• Formula
• Examples
• Calculator

What is the Percentage Change Formula?

The term “percentage change” refers to the measure of the change in the value of a given variable relative to its original value over a period of time. To put it simply, the percentage change is a simple mathematical concept that helps in determining the degree of change over a given period of time.

The formula for percentage change can be derived as the difference between the variable’s original value and the new value divided by its original value, which is then expressed in percentage. Mathematically, it is represented as,

Formula,

Example of Percentage Change Formula (With Excel Template)

Let’s take an example to understand the calculation of the Percentage Change Formula in a better manner.

Percentage Change Formula – Example #1

Let us take the example of a company’s total asset size to illustrate percentage change computation. As of December 31, 2018, the total asset size stood at $375 million compared to $365 million a year ago. Next, calculate the percentage change in the asset size.

Solution:

Percentage Change is calculated using the formula given below

Percentage Change = (New Value – Original Value) / Original Value * 100

• Percentage Change = ($375 million – $365 million) / $365 million * 100
• Percentage Change = 2.74%

Therefore, the company’s asset size has increased by 2.74% during the year.

Percentage Change Formula – Example #2

Let us take the example of Apple Inc.’s share price over the last seven trading days to illustrate percentage change computation. The following information has been extracted from Yahoo! Finance; calculate the daily percentage change in the share price based on the given information and comment on it.

Solution:

Percentage Change is calculated using the formula given below

Percentage Change = (New Value – Original Value) / Original Value * 100

Hence, Below all Calculations has been done Similarly.

From the above table, it can be seen that the percentage change in Apple Inc.’s equity share price has varied in the range of a decline of 2.31% to an increase of 2.84% over the last seven trading days. However, the share price has gone up four days and declined on two occasions resulting in an overall increase in the given period. In this case, the share price on the previous day is considered the original value, and the share price value today is taken as the new value, and this process is followed for each day. For instance, if today is 29 October 2019, then the previous day is 28 October 2019, and so the new value is $243.29, and the original value is $249.05.

Percentage Change Formula – Example #3

Let us take the example of the crude oil price movement over the last 15 years and comment on its price volatility. The following information has been extracted from Macro Trends. First, calculate the annual percentage change in crude oil prices.

Solution:

Percentage Change is calculated using the formula given below

Percentage Change = (New Value – Original Value) / Original Value * 100

Hence, Below all Calculations has done Similarly.

Therefore, it can be seen that the crude price has been very volatile in the last 15 years, with multiple occasions of the decline of more than 25% and a surge of more than 25%. From $61.06 per barrel in 2005, the price peaked to $98.83 in 2011, which eventually plummeted to $37.04 in 2015 again to go up to $56.20 in 2019.

Explanation

The Percentage Change Formula can be calculated by using the following steps:

Step 1: Firstly, figure out the value of the subject variable at the start of the given period, which is considered as the original value.

Step 2: Next, figure out the value of the same variable by the close of the given period, which is now the new value.

Step 3: Next, the change in the variable’s value over the period of time can be calculated by subtracting the original value (step 1) from the new value (step 2), as shown below.

Change in Value = New Value – Original Value

Step 4: Finally, the percentage change formula can be expressed as the change (increase or decrease) in value (step 3) divided by its original value (step 1), which is then multiplied by 100 as shown below.

Percentage Change = (New Value – Original Value) / Original Value * 100

Relevance and Uses of Percentage Change Formula

Although it is one of the easiest of analytical tools in vogue, it is still very important to understand its concept because it is the foundation technique from where all kinds of technical analysis start. The use of this formula is endless, right from tracking the price movement of individual securities to that of large complex market indexes, comparison of different currencies and their fluctuations, change in each line item of any financial statement, etc. Additionally, the degree or extent of percentage change is helpful in deciding whether the deviation in the subject variable requires any further investigation. The percentage change trend can indicate whether the variable is trending up or down or oscillating between certain values.

Percentage Change Formula Calculator

You can use the following Percentage Change Formula Calculator:

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