Updated July 25, 2023
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.
Simply put, the percentage change is a mathematical concept that helps determine the degree of change over a specified period. To derive the formula for percentage change, one subtracts the variable’s original value from the new value, divides the result by the original value, and then expresses the quotient as a percentage. Its mathematical representation is:
Examples of Percentage Change Formula (With Excel Template)
Here are some examples to better understand the calculation of the Percentage Change Formula:
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:
One calculates the Percentage Change using the formula given below:
Percentage Change = (New Value – Original Value) / Original Value × 100
Here:
- Percentage Change = ($375 million – $365 million) / $365 million × 100
- Percentage Change = 2.74%
Thus, 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:
One calculates the Percentage Change using the formula given below:
Percentage Change = (New Value – Original Value) / Original Value × 100
Below all calculations have been done similarly.
The table above shows that the percentage change in Apple Inc.’s equity share price has decreased from 2.31% to an increase of 2.84% over the last seven trading days. However, the share price has increased for four days and declined for two, resulting in an overall increase during the given period. To calculate the percentage change, the share price of the previous day is considered the original value, and the share price of the current day is taken as the new value, and this process is repeated for each day. For example, if today is October 29, 2019, then the previous day is October 28, 2019, and the new value is $243.29, while the original value is $249.05.
Percentage Change Formula – Example #3
Let us consider the example of crude oil price movements over the last 15 years and comment on its price volatility. The following data has been extracted from Macro Trends. The first step is to calculate the annual percentage change in crude oil prices.
Solution:
One calculates the Percentage Change using the formula given below:
Percentage Change = (New Value – Original Value) / Original Value × 100
Below all the calculations have been done similarly.
Thus, one can see that the crude price has been very volatile in the last 15 years, with multiple occasions of a decline of more than 25% and a surge of more than 25%. From $61.06 per barrel in 2005, the price peaked at $98.83 in 2011, which eventually plummeted to $37.04 in 2015, again to go up to $56.20 in 2019.
Explanation
One can calculate the Percentage Change Formula by following these steps:
Step 1: First, figure out the value of the subject variable at the beginning of the given period. This is the original value.
Step 2: Next, figure out the value of the same variable at the end of the given period. This is now the new value.
Step 3: Calculate the change in the variable’s value over the period of time 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 analytical tools in use, it is still essential to understand its concept because it is the fundamental technique from where all kinds of technical analysis start. The use of this formula is endless, ranging from tracking the price movement of individual securities to that of large complex market indexes, comparing different currencies and their fluctuations, examining each line item of any financial statement, and so on. 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, down, or oscillating between certain values.
Percentage Change Formula Calculator
One can use the following Percentage Change Formula Calculator:
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| Percent Change = |
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