Absolute Value Calculator
Calculate the absolute value of any number instantly. Find |a − b| distance, batch absolute values, complex number modulus, mean absolute deviation, and absolute error.
Absolute Value
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Distance from Zero —
Sign —
Extended More scenarios, charts & detailed breakdown ▾
|x|
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Sign —
Distance from Zero —
Professional Full parameters & maximum detail ▾
Complex Number Modulus
|a + bi| (complex modulus) —
Mean Absolute Deviation
Mean of 5 values —
Mean Absolute Deviation (MAD) —
Absolute Deviations from Mean —
Absolute & Relative Error
Absolute Error |measured − expected| —
Relative Error (%) —
How to Use This Calculator
- Enter any number (positive, negative, or zero) to see its absolute value instantly.
- Use Expression tab to calculate |a − b| — the distance between two numbers on a number line.
- Use Batch tab to find absolute values of 5 numbers at once.
- Use the Professional tab for complex number modulus, Mean Absolute Deviation (MAD), and absolute/relative error analysis.
Formula
|x| = x if x ≥ 0, −x if x < 0
|a + bi| = √(a² + b²) (complex modulus)
MAD = Σ|xᵢ − x̄| / n (mean absolute deviation)
Example
|−7| = 7 | |3 − 8| = |−5| = 5 | |3 + 4i| = √(9+16) = 5 (complex modulus)
Frequently Asked Questions
- The absolute value of a number is its distance from zero on the number line, always non-negative. |7| = 7, |−7| = 7, |0| = 0. Mathematically, |x| = x if x ≥ 0, and |x| = −x if x < 0.
- |a − b| is the absolute value of the difference between two numbers — the distance between them on the number line. |3 − 8| = |−5| = 5, meaning 3 and 8 are 5 units apart.
- For a complex number a + bi, the modulus |a + bi| = √(a² + b²). This is its distance from the origin in the complex plane. For 3 + 4i: |3 + 4i| = √(9+16) = √25 = 5.
- MAD measures the average absolute deviation of each value from the mean. For data {2, 4, 4, 4, 5}, mean = 3.8, deviations = {1.8, 0.2, 0.2, 0.2, 1.2}, MAD = (1.8+0.2+0.2+0.2+1.2)/5 = 0.72.
- Absolute error = |measured − expected|. Relative error = |measured − expected| / |expected| × 100%. If you measured 9.8 and expected 10.0: absolute error = 0.2, relative error = 2%.