# Angular Frequency

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omega =
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TylerJones.Angular Frequency
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c378a95b-2a1b-11e6-9770-bc764e2038f2

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

This equation, Angular Frequency, is listed in 1 Collection.