Radian
| Radian | |
|---|---|
| Unit system | SI derived unit |
| Unit of | Angle |
| Symbol | rad or c |
| 1 rad in ... | ... is equal to ... |
| milliradians | 1,000 milliradians |
| turns | 1/2π turn |
| degrees | ≈ 57.296° |
| gons | ≈ 63.662g |
The radian is the standard unit of angular measure, used in many areas of mathematics. The length of an arc of a unit circle is numerically equal to the measurement in radians of the angle that it ; one radian is just under 57.3 degrees (when the arc length is equal to the radius; expansion at 
). The unit was formerly an SI supplementary unit, but this category was abolished in 1995 and the radian is now considered an SI derived unit.
Separately, the SI unit of solid angle measurement is the steradian.
The radian is represented by the symbol rad. An alternative symbol is c, the superscript letter c, for "circular measure", or the letter r, but both of those symbols are infrequently used as it can be easily mistaken for a degree symbol (°) or a radius (r). So for example, a value of 1.2 radians could be written as 1.2 rad, 1.2 r, 1.2rad, or 1.2c.
Radian describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended at the center of a circle by an arc that is equal in length to the radius of the circle. More generally, the magnitude in radians of such a subtended angle is equal to the ratio of the arc length to the radius of the circle; that is, θ = s / r, where θ is the subtended angle in radians, s is arc length, and r is radius. Conversely, the length of the enclosed arc is equal to the radius multiplied by the magnitude of the angle in radians; that is, s = rθ.
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