Definition:Degree (Angular Measure)

Definition

Degrees are a measurement of plane angles symbolized by $^\circ$.

By definition, $1^\circ$ is equal to $\frac{1}{360}$ of a full rotation.

The use of degrees comes from the Babylonians, who used a sexagesimal (base 60) number system.

Degrees are usually the first way of measuring angles taught to mathematics students, usually at grade school.

Conveniently, the most commonly used angles in geometry (e.g. $30^\circ, 45^\circ, 60^\circ$) are all whole numbers when measured in degrees.

Also see

• Radians, from which we see:

$1^\circ = \frac {\pi} {180^\circ} \ \mathrm{rad} \approx 0.01745 \ 32925 \ 19943 \ 29576 \ 92 \ldots \ \mathrm{rad}$

Sources

• Murray R. Spiegel: Mathematical Handbook of Formulas and Tables (1968): $1.27 \ 5.14$