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. It is always a non-negative value. For example, both 5 and -5 have an absolute value of 5, because both are exactly 5 units away from zero. The absolute value of zero is 0.

Absolute value is denoted by two vertical bars surrounding the number or expression, like |x|. This concept is fundamental in mathematics and appears in algebra, geometry, calculus, and real-world applications such as distance measurement and error calculation.

How to Use the Absolute Value Calculator

Enter any real number (positive, negative, integer, or decimal) into the calculator. The absolute value is computed instantly using the formula:

The calculator shows the result along with a step-by-step breakdown explaining whether the number was positive (value stays the same) or negative (the sign is removed).

Properties of Absolute Value

• Non-negativity: |x| ≥ 0 for all real numbers x.
• Zero: |x| = 0 if and only if x = 0.
• Symmetry: |-x| = |x|. The absolute value of a number and its negative are equal.
• Triangle Inequality: |x + y| ≤ |x| + |y|.
• Multiplicativity: |x · y| = |x| · |y|.
• Distance: |x - y| represents the distance between x and y on the number line.

Examples of Absolute Value

Applications of Absolute Value

Absolute value is used in many areas of mathematics and science:

• Distance: Calculating the distance between two points on a number line or in coordinate geometry.
• Error Analysis: Measuring the magnitude of error without regard to sign.
• Programming: The Math.abs() function in JavaScript and similar functions in other languages returns the absolute value.
• Physics: Representing magnitudes of vectors, speeds, and other scalar quantities.
• Finance: Calculating absolute returns or deviations from expected values.

Frequently Asked Questions