Absolute Value Calculator
Calculate the absolute value of positive, negative, and decimal numbers instantly. Get the result with a clear calculation and number-line explanation.
Calculate Absolute Value
What Is Absolute Value?
Absolute value represents the distance of a number from zero on the number line. Because distance cannot be negative, an absolute value is always zero or positive.
The absolute value of -8 is 8 because -8 is eight units away from zero.
How to Use This Calculator
Finding an absolute value only requires entering the number you want to evaluate.
- Enter a number in the input field.
- Click the Calculate button.
- View the absolute value.
- Review the calculation explanation.
- Use the number line to understand the distance from zero.
How Does the Absolute Value Calculator Work?
The calculator determines the distance between the entered number and zero. If the number is positive, its absolute value remains unchanged. If the number is negative, the negative sign is removed.
Zero has an absolute value of zero because it is already located at zero on the number line.
|-12| = 12
|7| = 7
|0| = 0
|-3.5| = 3.5
Absolute Value Formula
The absolute value of a number x is written as |x|. It represents the non-negative distance of x from zero.
Positive and Negative Numbers
Positive numbers already have a non-negative value, so taking their absolute value does not change them.
Negative numbers become positive when their absolute value is calculated.
|15| = 15
|-15| = 15
Where Is Absolute Value Used?
Absolute value is useful in many areas of mathematics and practical calculations.
- Distance calculations
- Algebraic equations
- Number-line problems
- Error and difference calculations
- Statistics and data analysis
- Computer programming and algorithms
Properties of Absolute Value
Absolute value follows several useful mathematical properties that make it important when working with equations and inequalities.
|x| ≥ 0 for every real number x.
|x| = |-x|.
|0| = 0.
The property |x| = |-x| means that opposite numbers have the same absolute value because they are the same distance from zero.