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### Plane Angle

#### degree

One circle of angle is also defined as 360 °C, that is 1°C = π/180 rad = 0.0174533 rad.

#### full circle

The full circle of angle is defined as 360 °C or 2π rad.

Non-SI unit of plane angle, also called grade, gon, or gradian. It is defined as 1/400 of a full circle. 100 grad is a right angle. Centigrad is hundredths of a grad. 1 gon is 0.9 degree or approximately 0.01570796 radian.

#### mil

A name derives from milliradian. A unit of angular measurement used in artillery and equal to 1/6400 of a complete revolution.

#### minute

One minute is defined as 1/60 of degree or π/10800 rad.

#### point

Nautical unit for angle. One circle makes up 32 points, one point is 360/32 degrees = 11.25 degrees.

The plane angle between two half-lines terminating at the same point is defined as the ratio of the length of the included arc of the circle (with its centre at that point) to the radius of that circle. According to the definition, the coherent unit for plane angle is number one, CGPM accepted the special name radian as the unit of plane angle instead of number one for convenient use. One radian (symbol rad) is the angle subtended at the center of a circle by an arc of circumference that is equal in length to the radius of the circle. 1 rad = r, 2π rad= 2πr, so one circle of circumference is corresponding to 2π rad of angle.

#### second

One second is defined as 1/60 of minute or π/64800 rad.

### Solid Angle

#### hemispere

The solid angle subtending an area of a half of sphere, equals 2π steradians.

#### octant

The solid angle subtending an area of one eighth of sphere, equals π/2 steradians.

#### sphere

Since the solid angle is defined as Ω= A/r². The surface of a sphere subtends an angle is 4πr²/r² = 4π steradians at its centre.

#### square degree

The unit of solid angle used in astronomical observations. Since one degree of plane angle equals π/180 radian, the solid angle is defined as Ω= A/r², 1 sr = 1 m²/m² = 1/(180/π)² deg² 1 sr = (π/180)² deg², hence one square degree is defined to be (π/180)² = 0.0003046174 steradian.

#### square minute

The unit of solid angle used in astronomical observations. One square minute is defined as (1/60)² = 1/3600 square degree.

#### square second

The unit of solid angle used in astronomical observations. One square second is defined as (1/60)² = 1/3600 square minute.