OK, we all know average people tend to use either degrees or turns to measure angles, whereas mathematicians use radians, some other people use gradians, mils, or both, and there are other standards besides (points for boxing the compass, quadrants for studying your geometry, etc.).
My question is, are any of these more or less popular based on region, the way SI units give way to Imperial and/or US units based on where you go in the world?
… Spaniards generally measure them in degrees (sexagesimal ones, the kind where a full circle is 360º), although we’re taught about radians and centesimal degrees in school… what’s a turn? 
I suppose if you say, “Rotate the wheel a quarter turn clockwise,” that would be equivalent to 90 degrees, but I’ve never heard anyone actually using that as a way of measuring degrees. Is this what the OP is referring to?
Degrees. I’ve never heard of “turns”.
I suppose the ‘turn’ system is so informal nobody recognizes it as a system of angle measure.
Two realms where angles are expressed differently are in grade (usually in % slope but other systems are used) and in roof slopes using a ratio. But they seem to be fairly universal in Western society. Anyone know if other cultures use their own versions for these?
So are you actually going to tell us what this “turn” system is, or is it a secret?
a turn is 360 degrees.
:smack:
That’s what happened to me, yes. Not only is it informal, but extremely imprecise. Quarter turns and half turns are on the same metrological league as pinches of salt and small amounts of sugar. I might use it to give instructions on how much to rotate something, but not to measure how much it was actually rotated.
One turn is 360°, smaller angles are expressed as fractions thereof, and direction is usually expressed in terms of either left-hand/right-hand or counterclockwise/clockwise (or, if you speak Commonwealth English, anticlockwise/clockwise).
It’s fundamentally equivalent to radians if you replace pi with tau.
There’s also “revolutions” and “cycles” for measuring rotations.
So you’d say “turn the wheel a quarter of a turn to the left”?
Actually my colleagues and I often use “turns” when working in the lab, when turning adjustment knobs on various instruments. Often one rotation of the knob doesn’t translate to a physical quantity, but we still want to record how far it was turned. I’ve been in situations where I was recording at a resolution of 1/16 turn.
I hadn’t really thought about it, but we do something similar around the lab and my house too. Except we do it in terms of “hours”. as in “I turned it about 4 hours clockwise/forward”. We find it works better for things more than a 6 hour turn to decrease ambiguity and works well in breaking up the circle into mentally recognized fractions.
My car’s navigation system gives turn directions as “Turn left” for a turn to 270 degrees, “Turn right” for a turn to 90 degrees, and the face of the clock for other turns (e.g., “Turn right in the direction of One O’clock” for a turn to 30 degrees).