[(v2 - v1) / |v1|] x 100%Percentage change is a significant concept in various fields such as finance, economics, and mathematics. It helps in comparing the relative increase or decrease of quantities over a specific period. For instance, businesses use percentage change calculations to analyze financial trends, including revenue growth and profit margins. Similarly, economists rely on percentage changes to assess the fluctuations in economic indicators such as inflation rates and GDP.
Calculating percentage change is relatively simple, but it is essential to approach it with the right method and formula. It requires two primary values: the initial or old value and the final or new value. To find the percentage change between these two values, one follows a three-step process, including finding the difference between the new and old values, dividing the result by the old value, and finally multiplying the outcome by 100.
In this article, we will carefully walk you through each step of the process, explaining how to calculate percentage change accurately. Our objective is to help you gain a clear understanding of this essential concept and apply it to real-world situations with confidence. So, let's dive into the details and start mastering the art of calculating percentage change.
Percentage change is a mathematical concept that helps us understand how a value has changed in relation to its initial value. It's often used to track growth, decline, or trends in various fields, such as finance, economics, or even personal growth. Calculating percentage change requires only two values: the initial value (V1) and the final value (V2). You also need a simple formula to find the percentage change:
Percentage Change = [(V2 - V1) / V1] x 100
In this formula, V2 refers to the final value, and V1 stands for the initial value. The formula calculates the difference between these two values then divides it by the initial value to get a ratio. Finally, multiplying by 100 expresses this ratio as a percentage.
To further illustrate the concept, let's consider an example:
An investor purchases a stock for $20, and after a few months, its value is now $25. To determine the percentage change, we can use the formula mentioned above:
Percentage Change = [(25 - 20) / 20] x 100
Percentage Change = (5 / 20) x 100
Percentage Change = 0.25 x 100
Percentage Change = 25%
This result tells us that the stock's value has increased by 25% since the investor first purchased it.
While working with percentages, it's essential to understand the difference between absolute change and relative change. Absolute change refers to the raw difference between two values, while relative change compares this difference to the initial value. Percentage change is a type of relative change that's expressed as a percentage.
To find the absolute change, simply subtract the initial value from the final value. Here is an example:
Absolute Change = Final value - Initial value
Absolute Change = 75 - 50
Absolute Change = 25
Relative change reflects the proportion of the absolute change to the initial value. Here's how to calculate it using the example above:
Relative Change = (Absolute Change / Initial value)
Relative Change = (25 / 50)
Relative Change = 0.5
Lastly, to convert the relative change into a percentage change, simply multiply by 100 and add the percentage sign. Using the previous example:
Percentage Change = Relative Change * 100
Percentage Change = 0.5 * 100
Percentage Change = 50%
The percentage change in this example is an increase of 50% from the initial value.