The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that category was abolished in 1995). The radian is defined in the SI as being a dimensionless unit, with 1 rad = 1. Its symbol is accordingly often omitted, especially in mathematical writing. Definition One radian is defined as the angle subtended from the center of a circle which intercepts an arc equal in length to the radius of the circle. More generally, the magnitude in radians of a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, , where is the subtended angle in radians, is arc length, and is radius. A right angle is exactly radians. The rotation angle (360°) corresponding to one complete revolution is the length of the circumference divided by the radius, which is , or . Thus, radians is equal to 360 degrees. The relation can be derived using the formula for arc length, . Since radian is the measure of an angle that is subtended by an arc of a length equal to the radius of the circle, . This can be further simplified to . Multiplying both sides by 360° gives . Unit symbol The International Bureau of Weights and Measures and International Organization for Standardization specify rad as the symbol for the radian. Alternative symbols that were in use in 1909 are c (the superscript letter c, for "circular measure"), the letter r, or a superscript , but these variants are infrequently used, as they may be mistaken for a degree symbol (°) or a radius (r). Hence an angle of 1.2 radians would be written today as 1.2 rad; archaic notations could include 1.2 r, 1.2, 1.2, or 1.2. In mathematical writing, the symbol "rad" is often omitted. When quantifying an angle in the absence of any symbol, radians are assumed, and when degrees are meant, the degree sign is used. Dimensional analysis Plane angle is defined as , where is the subtended angle in radians, is arc length, and is radius. One radian corresponds to the angle for which , hence . However, is only to be used to express angles, not to express ratios of lengths