# Percentage Change Calculator

Find the percentage change between two values.

=\frac{V_2\ {-\ V}_1}{\left|V_1\right|}\ \times\ 100

## How To Calculate Percentage Change

The percentage change formula is used to quantify the change between two values and express the change as a percentage.

A positive number means that the final value has increased compared to the initial value and a negative number means the final value has decreased when compared to the inital value.

The formula is:

Percentage\ Change=\ \frac{\Delta V}{\left|V_1\right|}\ \times\ 100

Where:

**ΔV** – Change between Initial Value and Final Value

**|V₁|** – Absolute Value of the Initial Value

An absolute value is the positive value of a number regardless of its sign. For example the absolute value of -3 is 3. This is important to remember when dealing with negative values as it will change the result.

The change between two values (ΔV) can be substituted to give the following:

Percentage\ Change=\frac{V_2\ {-\ V}_1}{\left|V_1\right|}\ \times\ 100

Where:

**V₁** – Initial Value

**V₂** – Final Value

|**V₁**| – Absolute Value of the Initial Value

Note that the order of the two values makes a big difference to the result so make sure you have labelled the initial value and the final value correctly.

An easier way to remember the formula is to think of the Initial Value ( V₁) as the ‘Old’ value and the Final Value (V₂) as the ‘New’ value:

Percentage\ Change=\frac{New\ -Old}{Old}\ \times\ 100

For a description of other variations of the formula – including how to find the initial value given the other variables – see our percentage change formula page.

To test your knowledge, see our examples which contain the solutions to various practice questions.

Remember to avoid common mistakes and misconceptions about the percentage change formula.