Degree is the most commonly used, elementary unit of angular measurement. Even though it is the most common unit in practice it is not the SI unit of angular measurement.

A degree (arc degree) is defined as 1/360th of the total angle of a circle. It is further divided into minutes (arc minutes) and seconds (arc seconds). One arc minute is 1/60th of a degree, and an arc second is 1/60th of an arc minute. Another method of subdivision is decimal degree, where one arc degree is divided into 100. One hundredth of a degree is known and symbolized by the term grad.

Radian

A radian is defined as the plane angle subtended by a circular arc of length, which is equal to its radius.

 

Radian is the standard unit of angular measurement, and it’s used in many areas of mathematics and its applications. Radian is also a derived SI unit of angular measurement. Radians are symbolized using the term rad behind the numeric values.

A circle forms an angle of 2π rad, and a semicircle forms an angle of π rad. A right angle is π/2 rad.

These relations allow conversion from degrees to radians and vice versa:

1^° = π/180 rad    90^° = π/2 rad    180^° = π rad    270^° = 3π/2 rad    360^° = 2π rad      

1 rad = 180°/π