# Angular Hertz

(This help is also available inside Numerari.)

Common applications involve working with periodic behavior expressed in both regular frequencies having units of Hz (hertz) and as angular frequencies having units of radians per second. In these applications, the regular frequency is interpreted as cycles per second, and this regular frequency can be converted to angular frequency by defining one cycle to be equal to 2pi radians. However, the standard definition of Hz is just reciprocal seconds and the information about one cycle corresponding to 2pi radians is not built into this general Hz unit. Thus, a direct conversion, while technically satisfying the rules of metric unit conversion, is not the conversion you want.

Normally, you have to include the 2π radian factor yourself to get the desired answer.

The 2π radian factor is also needed inside sinusoidal function arguments.

To help with these very common applications, Numerari includes an additional unit called the "angular hertz". This unit is defined to be 2pi radians per second. You can use this unit in any situation where a regular frequency must be converted to an angular frequency. The conversion will be done automatically without having to manually add a 2pi radian factor.