Angular Frequency

TylerJones.Angular Frequency

The Angular Frequency calculator computes the angular frequency based on the frequency.

INSTRUCTIONS: Choose units and enter the following:

• (ƒ) Frequency

Angular Frequency (ω): The calculator returns angular frequency in radians per second.  However, this can be automatically converted to compatible units via the pull-down menu.

The Math / Science

The Angular Frequency equation mathematically relates angular frequency (rad/s) to frequency (Hz).  To understand angular frequency, we should start with frequency.

Frequency is a measure of how often something happens.  If something happens repeatedly, then the time between each occurrence is called the period.  Frequency (f) is the inverse of the period (T):

• `f = 1/T`

To mathematically describe things that repeat themselves (like waves, springs, pendulums, and a whole lot else), we often use sine and cosine.  Sine and cosine repeat themselves every `2 pi`.  Therefore, we want a sine or cosine argument that increments by `2 pi` every time the wave (for example) should repeat itself.  To make that argument, we multiply the frequency by `2 pi`.  This sine/cosine argument is called the angular frequency (`omega`).

• `omega = 2 pi f`