Definition:Radians

Definition

Radians are a measurement 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 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:

From this, it can be shown that a full rotation measures $2 \pi \ \mathrm{rad}$.

Thus we see that:

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

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

Sources

• Murray R. Spiegel: Mathematical Handbook of Formulas and Tables (1968): $1.26, \ 5.13$