Absolute Value Calculator
The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. Denoted as |x|, the absolute value of a positive number is itself, and the absolute value of a negative number is its positive equivalent. For example, |7| = 7 and |-7| = 7. This calculator computes the absolute value of any real number and shows its position on a number line. Absolute value is used in mathematics, physics, and engineering to represent magnitudes, distances, and errors without regard to direction.
Absolute value formula
|x| = x, if x >= 0
|x| = -x, if x < 0
Example: |−5.7| = 5.7
|5.7| = 5.7
|0| = 0
Absolute value examples
| Number | Absolute Value | Interpretation |
|---|---|---|
| 5 | 5 | Distance from zero: 5 units |
| -5 | 5 | Distance from zero: 5 units |
| 0 | 0 | At zero |
| -3.5 | 3.5 | Distance from zero: 3.5 units |
| 100 | 100 | Distance from zero: 100 units |
Absolute value calculator: frequently asked questions
What is the absolute value?
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative. The absolute value is denoted as |x|. For example, |5| = 5 and |-5| = 5.
What is the symbol for absolute value?
Absolute value is denoted using vertical bars: |x|. Read as 'the absolute value of x' or 'the modulus of x'. For example, |-3| means the absolute value of -3.
What is the difference between absolute value and modulo?
Absolute value finds the distance from zero. Modulo (remainder) finds the remainder after division. For the number -7: |−7| = 7, but -7 mod 3 could be 2 or -1 depending on the definition used.
When is absolute value used?
Absolute value is used in: distances (always positive), error magnitude, financial calculations (regardless of profit/loss), physics (magnitude of vectors), and solving equations involving absolute values.
What is the absolute value of zero?
The absolute value of zero is zero: |0| = 0. Zero has no direction, and its distance from itself (zero) is zero.
Official sources
- Absolute value: NIST Special Publication 330.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.