Definition:Angle/Unit/Radian

Definition

The radian is a measure of plane angles symbolized either by the word $\radians$ or without any unit.

Radians are pure numbers, as they are ratios of lengths. The addition of $\radians$ is merely for clarification.

$1 \radians$ is the angle subtended at the center of a circle by an arc whose length is equal to the radius:

Value of Radian in Degrees

The value of a radian in degrees is given by:

$1 \radians = \dfrac {180 \degrees} {\pi} \approx 57.29577 \ 95130 \ 8232 \ldots \degrees$

This sequence is A072097 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).

Also see

• Full Angle measures $2 \pi$ Radians

Technical Note

The $\LaTeX$ code for \(\radians\) is \radians .

Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles: The origins of trigonometry

• For a video presentation of the contents of this page, visit the Khan Academy.