Absolute Value Calculator

Calculate the absolute value of any number. This calculator shows the positive distance from zero and provides step-by-step explanations.

Absolute Value |x|

42.5

|-42.5| = 42.5

What is Absolute Value?

The absolute value of a number is its distance from zero on a number line, regardless of direction. It's denoted by |x| and is always non-negative. For example, |-5| = |5| = 5.

Examples

|-7| = 7

|3.14| = 3.14

|-2.5| = 2.5

|0| = 0

Properties

  • Always non-negative
  • |x| = |-x|
  • |xy| = |x| × |y|
  • |x + y| ≤ |x| + |y|

What is Absolute Value?

The absolute value of a number is its distance from zero on a number line, regardless of direction. It's denoted by |x| and is always non-negative.

Examples:
|5| = 5
|-5| = 5
|0| = 0

Examples and Applications

Basic Examples

Positive Numbers

  • |5| = 5
  • |3.14| = 3.14
  • |0.001| = 0.001

Negative Numbers

  • |-5| = 5
  • |-3.14| = 3.14
  • |-0.001| = 0.001

Real-World Applications

Distance Calculations

If you're 5 miles west or 5 miles east of a point, the absolute distance is 5 miles in both cases.

|5| = |-5| = 5 miles

Temperature Difference

The temperature difference between 75°F and 65°F is the same as between 65°F and 75°F.

|75 - 65| = |65 - 75| = 10 degrees

Error Margin

If a measurement has an error of ±2 units, the absolute error is 2 units.

|+2| = |-2| = 2 units

Common Uses

  • Finding distances between points on a number line
  • Calculating error margins in measurements
  • Determining the size of a difference between two values
  • Working with vectors and magnitudes
  • Analyzing financial gains or losses
  • Computing temperature variations

Key Properties

  • The absolute value of any non-zero number is always positive
  • The absolute value of 0 is 0
  • |x| = |-x| for any number x
  • |xy| = |x| × |y|
  • |x/y| = |x| ÷ |y| (when y ≠ 0)