Absolute Value
Distance from zero
About This Calculator
The absolute value of a number is its distance from zero on the number line, always a non-negative result. It is used in error calculations, distances, statistics, and anywhere the magnitude of a quantity matters regardless of direction. The absolute value of a difference gives the distance between two numbers.
Formula
|x| = x if x >= 0
|x| = −x if x < 0
|a − b| = distance between a and b on the number line
Example Calculation
Find |−7|, |5|, and |3 − 10|.
- |−7| = −(−7) = 7
- |5| = 5
- |3 − 10| = |−7| = 7
|−7| = 7; |5| = 5; |3 − 10| = 7
Absolute Values
| x | |x| | x | |x| |
|---|---|---|---|
| -5 | 5 | 1 | 1 |
| -4 | 4 | 2 | 2 |
| -3 | 3 | 3 | 3 |
| -2 | 2 | 4 | 4 |
| -1 | 1 | 5 | 5 |
| 0 | 0 | 0 | 0 |
Frequently Asked Questions
Can absolute value ever be negative?
No. By definition, absolute value is always non-negative. |x| >= 0 for all real numbers x, and |x| = 0 only when x = 0.
How is absolute value used in real life?
Absolute value measures distance or magnitude: temperature change (|final − initial|), error in measurements, and profit/loss regardless of direction.
What is the absolute value of a complex number?
For a complex number a + bi, the absolute value (or modulus) is sqrt(a² + b²), which represents the distance from the origin in the complex plane.