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For a time, I thought Azimuth is always direction in degrees, 0 for local, geographic north, 90 for east etc.

Then, trying to observe moonrise I downloaded an app that gave azimuth in values between (if I recall correctly) -180 and 180, and I think "0" corresponded to south. I tried to read up on that and found very little fragmented information. I found other resources that frustrated me with numbers greater than 360, or provided values commonly associated with "West" for azimuth of moonrise and generally it took a bit of searching to find something with plain "degrees from north"

Could someone either post or provide a link to a comprehensive guide to various azimuth angle systems, when and where they are in use, and how to recognize which one is used?

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Just to add to answers, since you mention you saw values greater than 360, those would likely be in gon or gradian and go from 0 to 400. But you always have to pay attention to the unit as well, not just the figure. On top of degrees (°) and gradians (gon), some other often cited units are radians (rad or ^c) and turns (rev or rot). Converting them is now easy enough by simply Googling for `value unit to unit`, e.g. 200 deg to rad, or using Wolfram Alpha. ;) –  TildalWave Oct 14 '13 at 23:40

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There are many indeed.

It may be specified from South westwards(0° to 360°), or from North eastwards and westwards(180° to -180°).

The most popular one, as used by Roy and Clarke in "Astronomy : Principles and Practices" is to measure the azimuth from North eastwards 0° to 360°. For a southern hemisphere observer, this system changes to from South eastwards 0° to 360°.

With so much confusion, how do professional astronomers go about it? They simply specify the system they are using in a given document. Doesn't cause much trouble since the differences in all of the systems is by an angle of 180° or 360°. It just causes sign changes in all formula.

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Azimuth is conventionally calculated as a degree value between 0 (inclusive) and 360 (exclusive). North is assigned 0 (also by convention), which puts East at 90, South at 180, and West at 270.

Sometimes 0 is set to South intead of North. This is the traditional means of measuring solar azimuth, even though North is the most accepted convention.

Positive azimuths are noted when measuring east of 0, whether 0 is South or North. Negative azimuths are noted when measuring west of 0.

Sources:

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