# What is a radian?

To understand **what a radian is**, you need to carefully analyze the diagram shown. This diagram shows a circle of radius r. If starting from the point A on the circumference of the circle, we move to a point B, covering exactly the distance r, we will have formed an angle that will be represented as: ø (phi).

Then:

*“The radian is the angle that cover the portion of the circumference **which is equal
to the length of the radius of the circle”.*

The diagram shows a circle of radius r. If we make a full turn. If we start at point A and end at the same point A, we have rotated 360 degrees and as is known, the circumference of a circle is C = 2π r. Passing this value to degrees:

– 2 π r = 360

– ø = 360/2 π

– with π = 3.141592

– ø = 360 / 6.283185

– ø = 57.29578 degrees

In electronics is often better to express the frequency in radians per second (angular frequency)

## Angular frequency

The **angular frequency** is represented by the letter ω (radians per second). The relationship between the frecuency in Hertz and the angular frequency is: ω = 2πf.

where:

– ω = angular frequency

– π = 3.141592 …. (the Pi constant)

– f = frequency in hertz

It is also used to represent the phase angles in radians. Instead of saying 90 degrees out of phase, we say π/2 radians out of phase. 60 degrees out of phase means π/3 radians out of phase.

When we use the symbol π in our calculations, the results of operations are not accurate, because its value is always used rounded. If the π value appears several times, the resulting error is greater. This problem does not exist when we use radians.

In the following video we can see the **radian** and the number of times that it gets into a circle. Theoretically, in a circle (360 degrees) enters 2π radians which is about 6.28 times a radian.