📏 Absolute Value Calculator

What Is Absolute Value?

The absolute value of a number x, written |x|, is its distance from zero on the number line, regardless of direction. |5| = 5 and |−5| = 5. Absolute value is always non-negative. Formally: |x| = x if x ≥ 0, and |x| = −x if x < 0.

Properties of Absolute Value

Key properties include: |a × b| = |a| × |b|, |a/b| = |a|/|b| (b ≠ 0), |a + b| ≤ |a| + |b| (triangle inequality), and |a − b| represents the distance between a and b on the number line. Absolute value is used extensively in calculus, linear algebra, and error analysis.