Absolute Value Calculator

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Absolute Value Calculator

Find the non-negative absolute value of any finite real number and see how it relates to distance from zero.

Last updated: August 2026 | By Summa Calculator

Absolute Value Solver

Enter a real number.

The absolute value is the distance from zero, so it is always zero or positive.
Absolute Value
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Enter a number to calculate

What is Absolute Value?

The absolute value of a real number is its distance from zero on the number line. It is written with vertical bars, such as |x|.

Because distance is non-negative, |x| is always greater than or equal to zero. A positive number keeps its value, a negative number changes sign, and zero remains zero.

Absolute Value Notation

The symbols |x| represent the absolute value of x.

In other words, |x| means the distance between x and zero.

|5| = 5
|-5| = 5
|0| = 0

For any real number x, the absolute value is x when x is positive, -x when x is negative, and 0 when x is zero.

How to Calculate Absolute Value

  1. Enter any real number.
  2. If the number is negative, change its sign to positive.
  3. If the number is positive or zero, leave it unchanged.
  4. The result is the number's non-negative distance from zero.

The calculator performs this process instantly and returns a non-negative result.

Absolute Value Formula

  • |x| = x when x >= 0
  • |x| = -x when x < 0

This definition ensures that the result is never negative.

Absolute Value on a Number Line

A helpful way to understand absolute value is to think about distance.

  • The distance from 0 to 8 is 8 units.
  • The distance from 0 to -8 is also 8 units.

Although the numbers lie on opposite sides of zero, they have the same absolute value because they are the same distance away.

|8| = 8
|-8| = 8

Examples

Positive number: |15| = 15
Negative number: |-42| = 42
Zero: |0| = 0
Decimal value: |-3.75| = 3.75

When Is Absolute Value Useful?

Absolute value is useful whenever magnitude or distance matters but direction or sign does not.

  • Finding how far a coordinate is from zero.
  • Comparing the size of positive and negative numerical values.
  • Turning a signed numerical difference into a non-negative distance.
Distance between 2 and 5 = |2 - 5| = |-3| = 3

This calculator accepts a single numeric value. It does not parse algebraic expressions, solve absolute value equations or inequalities, or graph absolute value functions.

Frequently Asked Questions

Can the absolute value be negative?

No. Absolute value is a distance, so it is always zero or positive.

What is |0|?

|0| = 0 because zero is zero units away from itself.

Does this calculator accept decimals?

Yes. Positive and negative decimal values are supported.

Does this calculator accept scientific notation?

Yes. Scientific notation can be used as long as the value represents a finite real number.

Can I enter blank input?

No. Blank input is treated as invalid, preventing accidental calculations using missing values.

Why do positive and negative numbers sometimes have the same absolute value?

Absolute value measures distance from zero. Numbers that are equally far from zero have the same absolute value regardless of whether they are positive or negative.

Can I enter an expression such as |x - 3|?

No. This calculator evaluates one finite real number at a time; it does not parse variables or algebraic expressions.

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