Absolute Value Calculator

Get the absolute value of any number, or solve an absolute-value equation of the form |ax + b| = c.

Absolute value

How to Solve Absolute Value

Get |x| for a number, or solve an absolute-value equation.

1

Absolute value of a number

On the first tab, enter any number to get its absolute value — its distance from zero, always non-negative.

2

Solve an equation

On the second tab, enter a, b and c for |ax + b| = c. The equation splits into two cases.

3

Read the solutions

Each case is solved separately, giving up to two values of x. If c is negative there is no solution.

Frequently Asked Questions

What is absolute value?
The absolute value of a number is its distance from zero on the number line, ignoring sign. |−7.5| = 7.5 and |7.5| = 7.5. It is never negative.
How do you solve an absolute value equation?
An equation |ax + b| = c with c ≥ 0 splits into two: ax + b = c and ax + b = −c. Solve each for x. This calculator shows both cases.
Why does |ax + b| = c have no solution when c is negative?
An absolute value measures distance from zero, and a distance can never be negative, so |ax + b| can never equal a negative c. For example, |2x + 3| = −5 has no solution, because whatever x you choose the left-hand side is 0 or greater. The boundary case c = 0 is different: |ax + b| = 0 has exactly one solution, x = −b/a. So the equation has two solutions when c is positive, one when c is zero, and none when c is negative.
Is my data sent anywhere?
Nothing you type is sent anywhere. The absolute value calculator runs entirely in your browser with JavaScript, so the number or the |ax + b| = c equation you enter never leave your device. There is no account, no upload step and nothing is logged. The page keeps working offline once it has loaded.