Absolute Value Calculator
Find the absolute value of any number and solve absolute value equations of the form |x − h| = k. Covers distance from zero, step-by-step solutions, and both real and no-solution cases.
Tab 1 — Absolute Value: Enter any real number (positive, negative, or decimal) into the input field. The calculator instantly finds its absolute value (distance from zero) and shows the value as a number line visualization, the original vs. result comparison, and the mathematical definition applied step by step.
Tab 2 — Solve |x − h| = k: Enter h (offset) and k (right-hand side). The calculator evaluates whether k is negative (no solution), zero (one solution: x = h), or positive (two solutions: x = h + k and x = h − k). It shows both cases with full working.
Definition: |x| = x if x ≥ 0, and |x| = −x if x < 0. This means the absolute value of a number is always non-negative.
Solving |x − h| = k: • If k < 0: No real solution (absolute value is never negative). • If k = 0: One solution, x = h. • If k > 0: Two solutions, x = h + k and x = h − k.
Geometric interpretation: |x| represents the distance from x to the origin on the number line. |x − h| represents the distance from x to the point h.
Verified Precise