Absolute Value Calculator
Free absolute value calculator. Find the absolute value of any number or expression. Includes explanation, examples, and the absolute value formula.
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Absolute Value Calculator
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Comprehensive Guide & Practice
Master the mathematical principles, formulas, and step-by-step methods with worked examples and FAQs.
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1. What Is Absolute Value?
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative. Notation: |x| is read "the absolute value of x".
Definition: |x| = x if x ≥ 0, and |x| = −x if x < 0.
Examples: |−7| = 7. |7| = 7. |0| = 0. |−3.14| = 3.14.
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2. Absolute Value in Equations
When solving |x| = 5, there are two solutions: x = 5 OR x = −5, because both are 5 units from zero. When solving |x − 3| = 4: x − 3 = 4 → x = 7, OR x − 3 = −4 → x = −1.
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3. Real-World Applications
- Temperature difference: The absolute temperature difference between −10°C and 5°C = |−10−5| = 15 degrees.
- Error measurement: In science and engineering, absolute error = |measured − actual|.
- Distance: Distance is always positive — absolute value models this naturally.
See also: Rounding Calculator | Algebra Basics