# Percentage difference calculator - Formula and steps

### Percentage Difference Calculator

### How to work out percentage differences - Step by Step

To find the percent difference between two values x and y, use this formula:

Note: the "|" marks either side (called "bars"), represents the absolute value of the expression inside them. This operation always returns a positive value or zero (in the set of real numbers - ℝ).

### Examples of absolute values:

- |12| = 12
- |-12| = 12
- |2| = 2
- |-3| = 3
- |0| = 0

Using this tool you can find the percent difference between any two values. So, we think you reached us looking for answers to questions like:

1) What is the percentage difference between 10 and 12?

2) What is the percentage difference between 12 and 10?

3) What is the absolute difference between 10 and 12?

Or may be:

What is the percent difference between 10 and 12. See below the solution to these problems.

Where: x and y are two values of a give variable. Note that percent difference is not equivalent or equal to percent change. Percent change is used when comparing a new value to an old value where the old value is used as a reference. Percent difference is used just to compare two values without considering any order. It doesn't matter which of the two values is written first. That is why the absolute value^{(*)} is often used. Percent difference is also called relative percent difference.

(*) Note: absolute value means that we must consider always a positive value as for example: |1|=1 (absolute value of 1 is 1) and |-1|= 1 (absolute value of minus 1 is also 1). See more about percent difference here.

Here are the solutions to the questions stated above:

### 1) What is the percentage difference between 10 and 12?

Use the above formula to find the percent difference between two numbers. So, replacing the given values, we have the percent difference equation

Where: y = 10 and x = 12, so |y| = 10 and |x| = 12

### 2) What is the percentage difference between 12 and 10?

As we can see, the answer for questions 1) and 2) are the same. That is because when we talk about diference in percentage, the order of the two values doesn't matter because the formula takes the absolute value of the diference divide by the mean value of each value.

### 3) What is the absolute difference between 10 and 12?

This problem is not about percent difference, but about absolute difference:

The absolute difference of two real numbers x, y is given by |x − y|, the absolute value of their difference. The minus sign denotes subtraction and |z| means absolute value. Absolute difference describes the distance between the points corresponding to x and y on the real line.

Now that you know what is absolute difference, The solution is very simple: