Absolute Value Calculator

Absolute Value is evaluated from Number or Value, a and b. The calculation reports Absolute Value |x|, Distance from 0 and Equation Solution x₁.

Results

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About the Absolute Value Calculator

Absolute Value is treated here as a quantitative relation between Number or Value, a, b and c and Absolute Value |x|, Distance from 0, Equation Solution x₁ and Equation Solution x₂.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
|x| = x if x >= 0, else -x
|ax + b| = c → ax + b = ±c → x = (±c - b)/a

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

|x| = x if x >= 0, else -x
|ax + b| = c → ax + b = ±c → x = (±c - b)/a

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Temperature Change Magnitude

Inputs

number: -23.5
Absolute Value |x|: 23.5. Distance from 0: 23.5

With Number or Value = -23.5 as the stated inputs, the result is Absolute Value |x| = 23.5 and Distance from 0 = 23.5. Each value corresponds to the declared output fields.

Example 2: Solve |2x + 3| = 7

Inputs

number: 0 a_val: 2 b_val: 3 c_val: 7
Absolute Value |x|: 0. Distance from 0: 0. Equation Solution x₁: 2. Equation Solution x₂: -5

With Number or Value = 0, a = 2, b = 3 and c = 7 as the stated inputs, the result is Absolute Value |x| = 0, Distance from 0 = 0 and Equation Solution x₁ = 2. Each value corresponds to the declared output fields.

Example 3: Error Tolerance — Manufacturing

Inputs

number: -0.003
Absolute Value |x|: 0.003. Distance from 0: 0.003

With Number or Value = -0.003 as the stated inputs, the result is Absolute Value |x| = 0.003 and Distance from 0 = 0.003. Each value corresponds to the declared output fields.

Example 4: Distance Between Points on a Line

Inputs

number: -8
Absolute Value |x|: 8. Distance from 0: 8

With Number or Value = -8 as the stated inputs, the result is Absolute Value |x| = 8 and Distance from 0 = 8. Each value corresponds to the declared output fields.

Common Use Cases

  • Find |x| for any real number
  • Calculate distance between two points on a number line
  • Solve |ax + b| = c equations
  • Find error magnitude in measurements