Definition:Angle/Unit/Radian

Definition

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

Radians are pure numbers, as they are ratios of lengths. The addition of $\mathrm{rad}$ is merely for clarification.

$1 \ \mathrm{rad}$ 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:

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

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

Sources

• 2008: Ian Stewart: Taming the Infinite ... (previous) ... (next): Chapter $5$: Eternal Triangles
• For a video presentation of the contents of this page, visit the Khan Academy.