Absolute Value Calculator
The absolute value of a number — its distance from zero, without a sign — and the distance between two numbers.
The absolute value |x| is x with any minus sign removed: |−7| and |7| are both 7.
How the absolute value calculator works
The absolute value |x| is x with any minus sign removed: |−7| and |7| are both 7. Geometrically it is the distance from x to zero on the number line, which is why it is never negative.
The same idea gives the distance between any two numbers as |a − b|. That form is worth knowing because it is symmetric — |a − b| equals |b − a| — so it answers "how far apart" without you having to decide which came first.
Formula: |x| = x if x ≥ 0, otherwise −x; distance = |a − b|
Worked examples
| Inputs | Absolute value | Note |
|---|---|---|
| The absolute value of −7.5 | 7.5 | 7.5 |
| How far apart are −7.5 and 3? | 7.5 | 10.5 |
| A positive number is unchanged | 12 | 12 |
FAQFrequently asked questions
What is the absolute value of a negative number?
The same number without the minus sign: |−7.5| is 7.5.
Can an absolute value be negative?
No. It measures distance from zero, and distance is never negative.
What is |0|?
Zero. It is the only number that is its own absolute value and its own opposite.
Why is |a − b| the distance?
Because subtracting gives the gap and the absolute value throws away the direction, leaving only how far apart they are.
How do I solve |x| = 5?
Two solutions, x = 5 and x = −5, because both are five units from zero.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Common Core State Standards — Mathematics — the terms and methods taught in US schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.