Turn (angle)

"360 degrees" and "360°" redirect here. For other uses, see 360 degrees (disambiguation).

Turn
Counterclockwise rotations about the center point starting from the right, where a complete rotation corresponds to an angle of rotation of 1 turn.
General information
Unit ofPlane angle
Symboltr, 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

The turn (symbol tr or pla) is a unit of plane angle measurement that is the measure of a complete angle—the angle subtended by a complete circle at its center. One turn is equal to 2π radians, 360 degrees or 400 gradians. As an angular unit, one turn also corresponds to one cycle (symbol cyc or c)[1] or to one revolution (symbol rev or r).[2] Common related units of frequency are cycles per second (cps) and revolutions per minute (rpm).[a] The angular unit of the turn is useful in connection with, among other things, electromagnetic coils (e.g., transformers), rotating objects, and the winding number of curves. Subdivisions of a turn include the half-turn and quarter-turn, spanning a straight angle and a right angle, respectively; metric prefixes can also be used as in, e.g., centiturns (ctr), milliturns (mtr), etc.

Because one turn is radians, some have proposed representing 2π with a single letter. In 2010, Michael Hartl proposed using the Greek letter (tau), equal to the ratio of a circle's circumference to its radius () and corresponding to one turn, for greater conceptual simplicity when stating angles in radians.[3] This proposal did not initially gain widespread acceptance in the mathematical community,[4] but the constant has become more widespread,[5] having been added to several major programming languages and calculators.

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 a full turn. It is represented by the symbol N. (See below for the formula.)

  1. ^ Cite error: The named reference Fitzpatrick_2021 was invoked but never defined (see the help page).
  2. ^ Cite error: The named reference IET_2016 was invoked but never defined (see the help page).
  3. ^ Cite error: The named reference Hartl_2019 was invoked but never defined (see the help page).
  4. ^ Cite error: The named reference Telegraph_2011 was invoked but never defined (see the help page).
  5. ^ Cite error: The named reference McMillan_2020 was invoked but never defined (see the help page).


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