Absolute Value Calculator

About the Absolute Value Calculator

The absolute value of a number is its distance from zero on the number line, without considering which direction from zero the number lies. This calculator helps you find the absolute value (modulus) of any real number, whether positive, negative, or zero.

What is Absolute Value?

In mathematics, the absolute value or modulus of a real number x, denoted |x|, is the non-negative value of x without regard to its sign. That is, |x| = x if x is positive, |x| = −x if x is negative, and |0| = 0.

Absolute Value Formula:

For any real number x, the absolute value is defined as:

|x| = {
  x, if x ≥ 0
  −x, if x < 0
}

Properties of Absolute Value

Absolute value has several important properties that make it useful in mathematics:

• Non-negativity: |x| ≥ 0 for all real numbers x
• Positive-definiteness: |x| = 0 if and only if x = 0
• Multiplicativity: |xy| = |x||y| for all real numbers x and y
• Subadditivity: |x + y| ≤ |x| + |y| (the triangle inequality)

Applications of Absolute Value

Absolute values are used in various mathematical and real-world contexts:

• Measuring distances (always non-negative)
• Error calculations in statistics
• Solving equations and inequalities
• Complex number modulus calculations
• Vector magnitudes in physics

How to Use This Calculator

To find the absolute value of any number:

1. Enter the number in the input field (positive, negative, or zero)
2. Select your preferred result format (decimal, fraction, or scientific notation)
3. Click "Calculate Absolute Value"
4. The result will show the absolute value of your input number
5. The number line visualization will display the position of your number and its absolute value