Absolute Value Calculator

Absolute value gives the distance of a number from zero on the number line. It is always non-negative.

|x| = x, if x ≥ 0

|x| = −x, if x < 0

Examples:

• |5| = 5
• |−5| = 5
• |0| = 0
• |−3.7| = 3.7

Properties of absolute value:

• |x| ≥ 0 for all x
• |x| = 0 only when x = 0
• |x × y| = |x| × |y|
• |x + y| ≤ |x| + |y| (triangle inequality)
• |x − y| gives the distance between x and y

Common uses:

• Finding distance between two points
• Error measurement (deviation from expected value)
• Defining neighborhoods in calculus (|x − a| < ε)