Absolute Value Calculator
Calculate the absolute value of any number, find the distance between two points on the number line, or solve absolute value equations of the form |x - a| = b. Get instant results with clear explanations.
The absolute value of a number represents its distance from zero on the number line, regardless of direction. It is always non-negative. The absolute value of -5 is 5, and the absolute value of 5 is also 5.
Mathematical Definition
|x| = x if x >= 0, and |x| = -x if x < 0. In other words, the absolute value strips away the sign.
Distance Between Numbers
The distance between two numbers a and b on the number line is |a - b|. For example, the distance between -3 and 5 is |-3 - 5| = |-8| = 8.
Absolute Value Equations
Equations like |x - a| = b have two solutions (when b > 0): x = a + b and x = a - b. If b = 0, there is one solution (x = a). If b < 0, there is no solution because absolute value is never negative.