Turn (angle)
One turn (symbol tr or pla) is a unit of plane angle measurement equal to 2π radians, 360 degrees or 400 gradians. Thus it is the angular measure subtended by a complete circle at its center.
| Turn | |
|---|---|
Counterclockwise rotations about the center point where a complete rotation corresponds to an angle of rotation of 1 turn. | |
| General information | |
| Unit of | Plane angle |
| Symbol | tr, pla, rev, cyc |
| Conversions | |
| 1 tr in ... | ... is equal to ... |
| radians | 2π rad ≈ 6.283185307... rad |
| milliradians | 2000π mrad ≈ 6283.185307... mrad |
| degrees | 360° |
| gradians | 400g |
Subdivisions of a turn include half-turns and quarter-turns, spanning a semicircle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.
As an angular unit, one turn also corresponds to one cycle (symbol cyc or c) or to one revolution (symbol rev or r).
In the ISQ, an arbitrary "number of turns" (also known as "number of revolutions" or "number of cycles") is formalized as a dimensionless quantity called rotation, defined as the ratio of a given angle and the full turn.
Common related units of frequency are cycles per second (cps) and revolutions per minute (rpm).