Definition
The solar azimuth is the angle, measured clockwise along the horizon from true north, between north and the point on the horizon directly below the sun. Together with the elevation angle it fixes the sun's position in the sky.
Not everyone measures from north. Astronomical texts and the NREL algorithm internally measure from south, positive to the west; some solar-engineering books use ±180° from south. This site always gives azimuth from north, clockwise, 0–360° — the same as a compass. Subtract 180° to convert to the south-based convention.
Formula
With latitude φ, declination δ and hour angle H (15° per hour from solar noon, negative in the morning):
A = atan2( sin H, cos H · sin φ − tan δ · cos φ ) + 180°
The two-argument arctangent puts the result in the right quadrant without the usual "if afternoon, subtract from 360°" correction. Sunrise and sunset azimuths follow from the moment the sun crosses the horizon:
cos Arise = sin δ / cos φ
How far it swings
At the equinoxes the sun rises almost exactly in the east (90°) and sets in the west (270°) everywhere on Earth. At the solstices the rising point moves north and south, and the higher the latitude, the further it moves. At 50° N the sun rises at about 52° (north-east) in June and about 128° (south-east) in December — a swing of 76° along the horizon. Above the Arctic Circle it eventually circles the whole horizon without setting.
At solar noon the azimuth is 180° in the northern mid-latitudes and 0° in the southern. Between the tropics the noon sun can be in either half of the sky, depending on the season.
Why it matters
- Panel orientation. The ideal panel azimuth faces the equator: 180° north of the tropics, 0° south of them.
- Shading. An obstacle only shades a panel when the sun's azimuth is behind it. The sun map draws the sunrise, sunset and current azimuth over your site.
- Architecture and photography. Window placement, the direction of the evening light, and where the sun sets behind a landmark.
For hour-by-hour values at your location, use the sun path diagram, or open any place page.