In physics, angular frequency ω (also referred to by the terms angular speed, radial frequency, circular frequency, orbital frequency, and radian frequency) is a scalar measure of rotation rate. Angular frequency (or angular speed) is the magnitude of the vector quantity angular velocity. The term angular frequency vector Failed to parse (Missing texvc executable; please see math/README to configure.): \vec{\omega}

One revolution is equal to 2π radians, hence

where

In SI units, angular frequency is normally presented in radians per second, even when it does not express a rotational value. From the perspective of dimensional analysis, the unit Hertz (Hz) is also correct, but in practice it is only used for ordinary frequency f, and almost never for ω. This convention helps avoid confusion.

In digital signal processing, the angular frequency may be normalized by the sampling rate, yielding the normalized frequency.

For example

where x is displacement from an equilibrium position.

Using 'ordinary' revolutions-per-second frequency, this equation would be