Absolute Value Calculator

Absolute Value Calculator

Find the absolute value, or magnitude, of any real number.

Last updated: June 2026 | By Patchworkr Team

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?

Absolute value describes a number's distance from zero on a number line, regardless of whether the number is positive or negative.

Because distance cannot be negative, the absolute value of a real number is always zero or positive.

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, remove the negative sign.
  3. If the number is positive or zero, leave it unchanged.
  4. The result is the absolute value, or magnitude, of the number.

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

Absolute Value in Expressions

Absolute value can also be applied to expressions rather than individual numbers.

|x - 3|

This expression represents the distance between x and 3 on a number line.

If x = 10:

|10 - 3| = 7

If x = 1:

|1 - 3| = 2

Absolute value removes direction and keeps only the distance.

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.

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