Degree (angle)

In mathematics, a degree is a common way to measure plane angle. It is written with the symbol ${\displaystyle ^{\circ }}$, where ${\displaystyle 360^{\circ }}$ corresponds to the entire circle.^[4][5][6]

Degree
One degree (shown in red) and 89 degrees (shown in blue)
General information
Unit system	Non-SI accepted unit
Unit of	Angle
Symbol	°[1][2] or deg[3]
Conversions
1 °[1][2] in ...	... is equal to ...
turns	${\displaystyle {\overline {360}}}$ turn
radians	${\displaystyle {\frac {\pi }{180}}}$ rad
gons	${\displaystyle {\frac {10}{9}}}$g

It is not an SI unit. The SI uses radian to measure plane angle. However, according to the SI brochure, it is an accepted unit by SI.^[7]

History

The actual reason of choosing the degree as a way to measure plane angle is unknown. One theory says that it is related with the fact that a year is approximately 360 days.^[5] Some ancient calendars, for example the Persian calendar and the Babylonian calendar used 360 days for a year.

Another theory says that the Babylonians divided the circle using the angle of an equilateral triangle. The angle was then divided into 60 parts. This is because they used sexagesimal or base-60 numeral system.^[8][9]

Related pages

• Degree of a polynomial