Definition
Azimuth is the angle along the horizon between a reference direction and the vertical circle passing through a celestial object. Together with altitude, the height above the horizon, it locates an object in the local sky: azimuth says which way to face, altitude how high to look.
Azimuth runs from 0° to 360°. It depends on the observer's position and changes continuously as the Earth turns, unlike right ascension and declination, which stay attached to the stars.
Two conventions
Navigation, surveying and most planetarium software count azimuth from north through east. Astronomical Algorithms, following an older astronomical tradition, counts it from south through west:
| Direction | From north (navigation) | From south (Meeus) |
|---|---|---|
| North | 0° | 180° |
| East | 90° | 270° |
| South | 180° | 0° |
| West | 270° | 90° |
Converting between the two is a matter of adding or subtracting 180°. Always check the convention before comparing azimuths from two sources: an error of 180° is the most common mistake with horizontal coordinates. The horizon views on this site label the cardinal points directly, so the convention is never ambiguous.
Computing azimuth
With the observer's latitude φ, the object's declination δ and its local hour angle H (local sidereal time minus right ascension), Meeus gives:
tan A = sin H / (cos H · sin φ − tan δ · cos φ)A is measured from south, westward. The quadrant must be resolved with the signs of the numerator and the denominator, using the two-argument arctangent atan2 found in every programming language. Adding 180° gives the azimuth from north.
Example: from Paris (φ = 48.86° N), a star with δ = +20° and H = 3 h (45°) is at A = 67.5° from south, that is 247.5° from north, in the west-southwest.
Where the Sun rises and sets
Ignoring refraction and the size of the Sun's disc, the azimuth of sunrise measured from north is given by cos A = sin δ / cos φ. It depends strongly on the season and on the latitude:
| Latitude | June solstice | Equinoxes | December solstice |
|---|---|---|---|
| 0° | 66.6° | 90° | 113.4° |
| 30° | 62.7° | 90° | 117.3° |
| 40° | 58.7° | 90° | 121.3° |
| 50° | 51.8° | 90° | 128.2° |
| 60° | 37.3° | 90° | 142.7° |
At the equinoxes the Sun rises due east and sets due west everywhere. At 60° N the June sunrise is in the northeast and the December sunrise almost in the southeast. Many monuments, from Stonehenge to the Karnak temples, are aligned on these solstice azimuths.
True north and magnetic north
Astronomical azimuths are measured from true (geographic) north, the direction of the celestial pole. A magnetic compass points to magnetic north, which differs by the magnetic declination: a few degrees in western Europe, more than 10° in much of North America, and changing by a fraction of a degree per year.
To align a telescope mount or a sundial, correct the compass reading with the local magnetic declination, or better, use the Sun: at local apparent noon, it is exactly due south (or due north in the southern hemisphere).
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Frequently asked questions
Is azimuth measured from north or south?
Usually from north, through east (navigation, most software). Meeus's Astronomical Algorithms measures it from south, through west. The two differ by exactly 180°.
Does the Sun always rise in the east?
Only at the equinoxes. In summer it rises north of east and in winter south of east, by up to 23° at the equator and much more at high latitudes.
What is the difference between azimuth and bearing?
In practice they are the same idea: a horizontal direction measured clockwise from north. Azimuth is the term used for celestial objects, bearing in navigation and surveying.
