Absolute Value Calculator

Calculate the absolute value of any real number or expression, returning the non-negative magnitude.

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Result

Enter a number Please enter a numeric value to calculate its absolute value.

Also in Functions

Algebra

Absolute value: distance from zero on the number line

The absolute value calculator returns the non-negative magnitude of any real number or expression. Enter a value to instantly see its distance from zero, regardless of sign.

What is absolute value?

The absolute value of a number is its distance from zero on the number line, without regard to direction. For example, both 5 and -5 have an absolute value of 5 because each is five units from zero.

Absolute value is written with vertical bars: |x|. It is always non-negative. For any positive number or zero the absolute value equals the number itself; for any negative number it equals the number with the sign flipped.

|x| = x if x >= 0, |x| = -x if x < 0

The piecewise definition of absolute value.

Applications

Absolute value appears throughout mathematics, science, and engineering. It is used to measure error, define distance in coordinate geometry, and set up piecewise equations. In statistics, mean absolute deviation relies on absolute values of differences from the mean.

Frequently asked questions

Can absolute value ever be negative?

No. By definition, absolute value is always zero or positive. The absolute value of zero is zero, and the absolute value of every nonzero number is positive.

What is the absolute value of a complex number?

For a complex number a + bi, the absolute value (modulus) is the square root of a squared plus b squared. This calculator handles real numbers only.

How is absolute value used in equations?

Absolute value equations like |x - 3| = 7 split into two cases: x - 3 = 7 and x - 3 = -7, giving x = 10 and x = -4.

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