Radian

"㎭" redirects here. Not to be confused with Rad (radiation unit).
For other uses, see Radian (disambiguation).

Radian
An arc of a circle with the same length as the radius of that circle subtends an angle of 1 radian. The circumference subtends an angle of 2π radians.
General information
Unit systemSI
Unit ofangle
Symbolrad, R[1]
Conversions
1 rad in ...... is equal to ...
   milliradians   1000 mrad
   turns   ⁠1/2π⁠ turn ≈ 0.159154 turn
   degrees   ⁠180/π⁠° ≈ 57.295779513°
   gradians   ⁠200/π⁠ grad ≈ 63.661977g

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. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius.[2] The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit,[2] defined in the SI as 1 rad = 1[3] and expressed in terms of the SI base unit metre (m) as rad = m/m.[4] Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.[5]

  1. ^ Cite error: The named reference Hall_1909 was invoked but never defined (see the help page).
  2. ^ a b International Bureau of Weights and Measures 2019, p. 151: "The CGPM decided to interpret the supplementary units in the SI, namely the radian and the steradian, as dimensionless derived units."
  3. ^ International Bureau of Weights and Measures 2019, p. 151: "One radian corresponds to the angle for which s = r, thus 1 rad = 1."
  4. ^ International Bureau of Weights and Measures 2019, p. 137.
  5. ^ Ocean Optics Protocols for Satellite Ocean Color Sensor Validation, Revision 3. National Aeronautics and Space Administration, Goddard Space Flight Center. 2002. p. 12.