Plane angles measurement systems

The two most common units of measurement for angles are degrees and radians.

In the degree system, the measurement unit is a 1-degree arc which is 1/360 of a circle (denoted as °).
There are 60 minutes in 1 degree (denoted as ’), and there are 60 seconds in 1 minute (denoted as ’’).

In astronomy, when measuring lesser plane angles, the angular unit same as a second is used. 1 second of arc (also denoted as ″). Along with a second arc, its fractional units are used: milliseconds, microseconds, and picoseconds.

The degree system is known since the days of Babylon. However, it is inconvenient due to its non-positionality for practical calculations, therefore at the end of the XVIII century in France, the grade was introduced as the main plane angle measurement unit with the introduction of the metric system. This system's plane angle is divided into 100 degrees ("grades"), degree into 100 centesimal minutes, and the centesimal minute into 100 centesimal seconds. Now, this system is most often used in geodetic measurements.

Radian is the basic plane angle measurement unit in mathematics. Radian is defined as an angular value of the arc of the unit length on the circle with radius = 1. That is, by circumferential length formula we get that there is radian in the circle.

Revolution or circle equal to 360 degrees.

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