Absolute Value Calculator
Enter any real number to find its absolute value — the distance from zero on the number line, always non-negative. The calculator also shows the sign, magnitude and how the value behaves in equations.
Enter a number
Enter a number and press Calculate |x|.
What absolute value means
The absolute value of a real number is its distance from zero on the number
line, regardless of direction. It is written with vertical bars:
|x|.
|x| = x if x ≥ 0
|x| = −x if x < 0
For example, |5| = 5 and |−5| = 5, because both 5
and −5 are exactly 5 units from zero. The result of an absolute value is
always non-negative.
Worked examples
Example 1 — Negative integer
|−17| = 17 because −17 is 17 units from zero.
Result: 17
Example 2 — Negative decimal
|−3.25| = 3.25
Result: 3.25
Example 3 — Already positive
|42| = 42 (no change)
Result: 42
Example 4 — Zero
|0| = 0
Result: 0
Where absolute value is used
- Distance: the distance between two points on a line is
|a − b|. - Error measurement: how far a measurement is from the true value, regardless of direction.
- Tolerance checks:
|measured − target| ≤ toleranceis a common pass/fail condition in manufacturing. - Complex numbers: the modulus of
a + biis√(a² + b²), an extension of absolute value. - Physics: magnitude of vectors, velocities and forces, ignoring direction.
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Frequently asked questions
No. Absolute value measures distance, and distance is never negative. The result is always zero or greater.
|0| = 0. Zero is exactly at zero distance from itself.
They are different operations. |x| returns the magnitude of x. −x flips the sign of x. For a negative x, they coincide (|−5| = 5 = −(−5)), but for a positive x they differ (|5| = 5, but −5 = −5).