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Calculation Machine

Absolute Value Calculator

Distance from zero, and |ax+b| equations.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
|x|
7.5
Solutions of |ax + b| = c
x = 8 or x = -2
Sign of x
negative
|x| squared
56.25

Quick answer

The absolute value of a number is its distance from zero, so it is always zero or positive.

The formula

|x| = x if x ≥ 0, else −x

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Value of x-7.5
  • a in |ax + b| = c2
  • b-6
  • c10

Result

  • |x|7.5
  • Solutions of |ax + b| = cx = 8 or x = -2
  • Sign of xnegative
  • |x| squared56.25

How to use the Absolute Value Calculator

  1. 1Enter a value to get its absolute value.
  2. 2Enter a, b and c to solve |ax + b| = c.
  3. 3Remember there are usually two solutions.

Frequently asked questions

Can absolute value be negative?

No, never — the result is always zero or positive.

Why two solutions?

Both a positive and a negative inside expression can have the same distance from zero.

About this calculator