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The percent change, also known as the percentage change or relative change, is a measure of how much a quantity has changed in percentage terms. It is commonly used in various fields, including finance, economics, and mathematics. The formula for calculating percent change is as follows:

$\text{Percent Change} = \left( \frac{\text{Final Value} - \text{Initial Value}}{\left| \text{Initial Value} \right|} \right) \times 100$

Here's a step-by-step explanation of each part of the formula:

1. Difference between Final and Initial Values:

   • Subtract the initial value from the final value. This represents the absolute change in the quantity.

     $\text{Absolute Change} = \text{Final Value} - \text{Initial Value}$

2. Relative Change:

   • Divide the absolute change by the absolute value of the initial value. This normalizes the change with respect to the initial value.

     $\text{Relative Change} = \frac{\text{Absolute Change}}{\left| \text{Initial Value} \right|}$

3. Convert to Percentage:

   • Multiply the relative change by 100 to express the result as a percentage.

     $\text{Percent Change} = \text{Relative Change} \times 100$

By following these steps, you can determine the percentage change between two values. The result will be positive if there is an increase and negative if there is a decrease. This formula allows for a standardized way to quantify the magnitude of change, making it useful for comparing changes across different scenarios and contexts.

Let's go through a quick example:

• Initial Value: $50
• Final Value: $75

$\text{Absolute Change} = 75 - 50 = 25$

$\text{Relative Change} = \frac{25}{\left| 50 \right|} = \frac{25}{50} = 0.5$

$\text{Percent Change} = 0.5 \times 100 = 50\%$

So, in this example, there is a 50% increase from $50 to $75.