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

Complex number +  i
Decimal places
Angle measure

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

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

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

See also polar form

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