# Arg, angle of complex number

Calculator for the angle of a complex number

## Complex number angle calculator

Enter a complex number to perform the angle calculation. Then click the 'Calculate' button.

The result can be displayed in degrees or radians.

Angle calculater

 Input Complex number + i Decimal places 0 1 2 3 4 6 8 10 Results Angle Angle measure Degree Radian

Angle φ = 45°

## Description of the angle of a complex number

Every complex number $$z$$ can be represented as a vector in the Gaussian number plane. This vector is uniquely defined by the real part and the imaginary part of the complex number $$z$$.

A vector emanating from the zero point can also be used as a pointer. This pointer is uniquely defined by its length and the angle $$φ$$ to the real axis (x).

Positive angles are measured counterclockwise, negative angles are clockwise.

## Formula and example

$$\displaystyle θ = tan^{-1}\left(\frac{y}{x}\right)$$

$$\displaystyle θ = tan^{-1}\left(\frac{3}{4}\right) ≈ 36.87$$