Absolute Value Calculator
Calculate absolute values, distance between points, and understand absolute value properties. Free online absolute value calculator.
Distance Between Two Points
Absolute Value Properties
Definition: |x| = x if x ≥ 0, |x| = -x if x < 0
Non-negative: |x| ≥ 0 for all x
Identity: |x| = 0 ⟺ x = 0
Symmetry: |-x| = |x|}
Triangle Inequality: |x + y| ≤ |x| + |y|
Product: |xy| = |x| × |y|
Quotient: |x/y| = |x| / |y| (y ≠ 0)
Examples
|-5|=5
|3|=3
|-2.5|=2.5
|0|=0
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Last updated: January 2026
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Frequently Asked Questions
What is absolute value?
Absolute value is the distance of a number from zero on a number line, always expressed as a non-negative number. Written as |x|, it removes the sign: |5| = 5 and |-5| = 5. Think of it as 'how far from zero' regardless of direction.
How do I calculate absolute value?
If the number is positive or zero, the absolute value is the number itself. If negative, remove the minus sign. Examples: |7| = 7, |0| = 0, |-12| = 12, |-3.5| = 3.5. The result is always zero or positive.
What is absolute value used for in real life?
Absolute value measures magnitude without direction: distance traveled (you can't walk -5 miles), temperature differences (10°F difference whether warming or cooling), stock price changes, error margins in measurements, and calculating distances between any two points.
How do I solve absolute value equations?
For |x| = a (where a ≥ 0), the solutions are x = a or x = -a. Example: |x| = 5 means x = 5 or x = -5. For |x - 3| = 7, solve x - 3 = 7 (x = 10) and x - 3 = -7 (x = -4). If a < 0, there's no solution since absolute values can't be negative.
What is the triangle inequality?
The triangle inequality states |a + b| ≤ |a| + |b|. The absolute value of a sum is at most the sum of absolute values. Example: |3 + (-5)| = |-2| = 2, while |3| + |-5| = 3 + 5 = 8. This applies to distances: the direct path is never longer than going through an intermediate point.