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Calculator Answers

Absolute Value Calculator

Blake Boege
Written by Blake Boege · Founder, Calculator Answers

An absolute value calculator computes the non-negative magnitude of a real number or expression, representing its distance from zero on the number line. For positive numbers, the absolute value is the number itself; for negative numbers, the value is negated to become positive. It supports evaluating simple inputs and absolute differences between two values (|a - b|).

Calculate the absolute value |x| of any real number or evaluate distance expressions like |a - b| with steps.

Quick Answer

Calculate the absolute value of a single number or evaluate expression distances like |a - b|. Distance values are always non-negative.

Calculator mode

Enter any positive, negative, or zero value. · e.g. -7

Absolute Value

Absolute Value |x|

7

|-7| = 7

Input x-7
Absolute value |x|7

The absolute value of -7 is 7. It represents the distance of -7 from 0 on the number line. Since -7 is negative, we negate it to get a positive distance: -(-7) = 7.

Step-by-step calculation

Step 1:|x| = x if x ≥ 0
Step 2:|x| = -x if x < 0
Step 3:|-7| = 7
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Examples

|-5|

= 5

|3 - 10|

= |-7| = 7

|0|

= 0

How it works

The Concept of Absolute Value

Geometrically, the absolute value of a number is its distance from zero on the real number line. Distance is a physical measurement, which means it can never be negative.

Mathematical Definition

|x| = x (if x ≥ 0)

|x| = −x (if x < 0)

To compute roots alongside absolute values, visit our standard square root calculator or use our new cube root calculator for third-order root operations.

Properties of absolute values

  • Non-negativity: |x| ≥ 0 (distance is always positive or zero).
  • Symmetry: |−x| = |x| (opposite values are equidistant from zero).
  • Multiplicativity: |a × b| = |a| × |b|.
  • Triangle Inequality: |a + b| ≤ |a| + |b|.

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Frequently asked questions

The absolute value of a number represents its non-negative distance from zero on the number line. Regardless of whether the number is positive or negative, its absolute value is always positive (or zero). It is written with vertical bars, like |x|.

If a number x is positive or zero, its absolute value is x itself: |x| = x. If x is negative, we negate it to make it positive: |x| = −x. For example, |−5| = −(−5) = 5.

The absolute value of zero is zero: |0| = 0. This is because zero is a distance of exactly 0 units away from itself on the number line.

First compute the value inside the vertical bars (a − b), then take the absolute value of the result. For example, |3 − 10| = |−7| = 7. This represents the geometric distance between the two points 3 and 10 on a number line.