How to Calculate Absolute Value

The absolute value of a number is its distance from zero on the number line, always expressed as a non-negative value. The absolute value of a positive number is itself; the absolute value of a negative number is its positive counterpart.

The Formula

|x| = x    if x ≥ 0
|x| = −x   if x < 0

Examples

  • |5| = 5
  • |−5| = 5
  • |0| = 0
  • |−3.7| = 3.7
  • |√2| = √2 (since √2 > 0)

Absolute Value in Equations

To solve |x| = 7:

  • Case 1: x = 7
  • Case 2: x = −7

Both solutions work: |7| = 7 ✓ and |−7| = 7 ✓

To solve |2x − 3| = 11:

  • Case 1: 2x − 3 = 11 → 2x = 14 → x = 7
  • Case 2: 2x − 3 = −11 → 2x = −8 → x = −4

Absolute Value Inequalities

|x| < 5 means −5 < x < 5 (x is within 5 units of zero) |x| > 5 means x < −5 or x > 5 (x is more than 5 units from zero)

Applications

  • Error calculation: |measured − actual| gives the absolute error
  • Statistics: Mean absolute deviation uses |xᵢ − x̄|
  • Physics: Magnitude of velocity (speed) is |velocity|
  • Distance: Distance between two points on a number line is |a − b|

Use our absolute value calculator for any expression.