Processing...

`omega = 2 pi * f`

Enter a value for all fields

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 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`