Absolute Value Formula

by Yogi P - October 22, 2023

What is Absolute Value Formula?

Absolute Value Formula defines the distance between a given number and zero. Mathematically, it is represented by the absolute value of a number in jargon – where the absolute value of a number is always a positive value.

For example, the absolute value of -2 is 2, as it is positive two units away from zero on a number line.

Formula Explanation

The absolute value formula is given by the expression:

|x| = x, if x ≥ 0

|x| = –x, if x < 0

Here x is a given number, and |x| is the absolute value of x. Hence, if the given number is a positive value, the absolute value of that number will be the same as the given number itself.

On the other hand, if the given number is negative, then the absolute value of that number will be the negative of the value of the given number.

Use Cases

Absolute Value Formula is used in a wide variety of mathematical activities and real-world problems.

For example, in the study of linear equations, the formula is employed to simplify equations– specifically to convert a non-linear equation into a linear equation.

In geometry, the formula is used to measure the distance between two points in a coordinate space. In addition, Absolute Value Formula is also used to calculate time differences, surface area, daily rates, capital gains, and so forth.

Solved Example

Let’s consider an example to understand how the Absolute Value Formula is used. Say, we are given the number -14. We have to find the absolute value of -14.

According to the formula given above,

|x| = –x, if x < 0

As given number is x = -14,

The absolute value of -14 is

|x| = –(-14) = 14

Hence, the absolute value of -14 is 14.

Through this example, we can understand that the absolute value of negative numbers is their positive equivalent.