Absolute Value Calculator

What is Absolute Value?

The absolute value of a number is its distance from zero on a number line, regardless of direction. In other words, the absolute value represents the magnitude of a number without considering whether it is positive or negative. The absolute value is always non-negative, meaning it is either zero or a positive number.

The symbol used to represent the absolute value is a pair of vertical bars | |. For any number $x$, the absolute value is denoted as:

$$\text{Absolute Value}=\mathrm{\mid }x\mathrm{\mid }$$

If $x$ is a positive number or zero, the absolute value is simply $x$. If $x$ is a negative number, the absolute value is the positive equivalent of $x$.

Examples of Absolute Value Calculations

Let’s look at a few examples to understand how the absolute value is determined:

Example 1:

• Number: $x = 5$
  
• Calculation:
  • Since 5 is positive, the absolute value is $5$.
• Absolute Value: $|5| = 5$
  

Example 2:

• Number: $x = -7$
  
• Calculation:
  • Since -7 is negative, the absolute value is the positive equivalent, which is $7$.
• Absolute Value: $|-7| = 7$
  

Example 3:

• Number: $x = 0$
  
• Calculation:
  • The absolute value of zero is always $0$.
• Absolute Value: $|0| = 0$
  

Example 4:

• Number: $x = -15.2$
  
• Calculation:
  • Since -15.2 is negative, the absolute value is the positive equivalent, which is $15.2$.
• Absolute Value: $|-15.2| = 15.2$
  

In these examples, the absolute value represents how far the number is from zero on the number line, without considering its direction. Whether the number is positive, negative, or zero, the absolute value gives a non-negative measure of its magnitude.