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Absolute Value Calculator

Calculate absolute value for any real number, then explore definitions, formulas, equations, inequalities, and graphs. All math runs privately in your browser.

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Absolute value calculator: find |x| for any real number

Your number

Type integers, decimals, or negative values. Results update as you type.

Absolute value

...

Enter a number to compute |x|.

Using this calculator

  1. Type your number in the value field.
  2. Read |x| in the result panel.
  3. Check the formula line to see the notation.
  4. Tap Clear to reset the field.

What Is Absolute Value?

Absolute value measures how far a number is from zero on the number line, without regard to direction. We write |x| and read it as the absolute value of x.

Think of it as distance: |−7| and |7| both equal 7 because each point is seven units from zero. That distance interpretation is why absolute value appears in algebra, coordinate geometry, and real-world error checks.

Absolute value is defined for every real number. The result is always zero or positive, which makes it useful when you care about magnitude rather than sign.

  • Distance from zero

    The core meaning: |x| is how many units x lies from 0.

  • Sign removed

    Negative inputs become positive outputs; non-negative inputs stay the same.

  • Real-world use

    Temperature deviation, elevation change, and measurement error often use |x|.

Absolute Value Formula

|x| = x when x ≥ 0

|x| = −x when x < 0

Distance between two numbers a and b:

|a − b|

Compact form (same result for real x):

|x| = √(x²)

Quick samples:

|5| = 5 |−5| = 5 |0| = 0

The piecewise definition is what you apply by hand: keep non-negative numbers, flip the sign of negative numbers. The radical form is equivalent for real numbers and sometimes appears in proofs.

For coordinate problems, |x₁ − x₂| gives the distance between two points on a horizontal line. The calculator at the top of this page applies the single-number rule automatically.

How to Calculate Absolute Value

You can compute |x| mentally, on paper, in a spreadsheet, or with the on-page calculator. Each method should agree on the final non-negative value.

  1. Manual method

    Identify x. If x ≥ 0, |x| = x. If x < 0, |x| = −x. Example: |−12| = 12.

  2. Number line check

    Plot x and count units to zero. That count is |x|.

  3. Calculator method

    Enter x in the tool at the top of this page. The result updates instantly in your browser.

  4. Spreadsheet method

    In Excel or Google Sheets use =ABS(x) for a numeric cell.

  5. Shortcut

    If you already know x is negative, drop the minus sign. If x is already ≥ 0, copy x.

Absolute Value Examples

These worked examples cover common input types you will see in homework and tests.

8

Positive integer

Find |8|.

|8| = 8

Result: 8

−9

Negative integer

Find |−9|.

|−9| = 9

Result: 9

−3.2

Decimal

A sensor reads −3.2 units off target. Magnitude is |−3.2|.

|−3.2| = 3.2

Result: 3.2

−3/4

Fraction

Find |−3/4|.

|−3/4| = 3/4

Result: 3/4

0

Zero

Zero is on zero.

|0| = 0

Result: 0

x

Expression form

If x = −6, then |x| = |−6| = 6.

|−6| = 6

Result: 6

Absolute Value Equations

An absolute value equation includes |expression| and often has two solutions because the expression inside can be positive or negative.

The key idea: |A| = B (with B ≥ 0) means A = B or A = −B. If B is negative, there is no real solution.

Always isolate the absolute value first, then split into two linear equations. Check each solution in the original equation.

For deeper practice, read our absolute value equations guide.

  1. Isolate |...|

    Get the absolute value expression alone on one side.

  2. Split into two cases

    Set the inner expression equal to the positive value and equal to its opposite.

  3. Solve both equations

    Solve each linear equation separately.

  4. Verify

    Substitute every candidate back into the original equation.

Example: |x − 2| = 5

Solve |x − 2| = 5.

x − 2 = 5 → x = 7 OR x − 2 = −5 → x = −3

Solutions: x = 7 and x = −3

Absolute Value Inequalities

Inequalities with absolute value describe ranges on the number line. The pattern depends on whether you use < or >.

  • Less than: |x| < k

    The value sits within k units of zero. Solution: −k < x < k (interval notation: (−k, k)).

    |x| < 4 → −4 < x < 4

  • Greater than: |x| > k

    The value is farther than k units from zero. Solution splits: x < −k or x > k.

    |x| > 3 → x < −3 or x > 3

  • Interval notation

    Open intervals match strict inequalities (< or >). Closed endpoints apply when the inequality includes equality.

  • Graphing

    Plot the boundary points as open or closed circles, then shade the regions that satisfy the inequality.

Absolute Value Graph

The graph of y = |x| forms a V-shape with its vertex at the origin.

Absolute Value vs Distance

Absolute value and distance are closely related: |x| is the distance from x to 0 on a number line.

For two points a and b on a line, the distance between them is |a − b|. Order inside the bars does not change the distance: |a − b| = |b − a|.

In the plane, distance formulas use square roots, but horizontal or vertical separations still reduce to absolute value of a coordinate difference.

ConceptFormulaTypical use
|x|distance from 0Magnitude of one number
|a − b|distance on a lineGap between two values
Error / deviation|actual − target|How far off a measurement is

Absolute Value Calculator

Use the calculator in the hero section to find |x| for any single real number you enter.

  • One input field for the value x
  • Instant |x| result as you type
  • Formula line showing |x| = result
  • Sign note for negative, positive, or zero input
  • Private browser-only math (no upload)

Enter integers, decimals, or negative values. The tool applies the piecewise rule automatically so you can verify homework, lab data, or exam practice.

For equations, inequalities, or graphs, use the sections below and linked articles. The calculator focuses on evaluating |x| for one number at a time.

Need a refresher on the definition? Start with what is absolute value.

Back to calculator

Common Absolute Value Mistakes

Absolute Value in Algebra

Absolute value connects to several core algebra topics. Use these guides to go deeper after you can compute |x| confidently.

In linear equations and inequalities, absolute value creates piecewise conditions. In coordinate geometry, it measures horizontal and vertical separations.

Piecewise functions often use absolute value branches. Recognizing where the inside expression equals zero tells you where the graph may turn.

FAQs About Absolute Value

What is the absolute value of a negative number?

Flip the sign. Example: |−4| = 4 because −4 is four units from zero.

Can absolute value be negative?

No. By definition, |x| ≥ 0 for every real number x.

How do you solve |x| = 7?

Split into x = 7 or x = −7. Both values are seven units from zero.

What is the difference between |x| and |a − b|?

|x| is distance from zero. |a − b| is the distance between a and b on a number line.

Does the calculator solve equations?

The on-page tool evaluates |x| for one number. For equations, use the methods in the Absolute Value Equations section.

Can I enter decimals and fractions?

Yes. Enter decimal forms directly. For fractions, use decimal form or compute the fraction by hand and verify with the tool.

Does the site store my input?

No. All calculation runs locally in your browser.