Solar azimuth angle calculator from latitude, declination and hour angle

It reports an angle measured clockwise from true north together with a familiar sixteen-point compass direction. Enter all three angles in decimal degrees, using negative hour angles before local solar noon and positive values after noon. The calculation is deterministic, runs without network access, and is suitable for checking solar geometry used in daylighting, photovoltaic planning, shadow studies, and educational astronomy.

Enter the three solar-geometry angles correctly

Start with the observer's geographic latitude in decimal degrees. Northern latitudes are positive, southern latitudes are negative, and the allowed range runs from minus ninety to plus ninety degrees. Solar declination describes the sun's angular position north or south of the celestial equator. It changes through the year and is positive when the sun is north of that equator. The hour angle describes time relative to local solar noon rather than civil clock noon. Use zero at local solar noon, negative values during the solar morning, and positive values during the solar afternoon. Fifteen degrees of hour angle corresponds to approximately one hour of solar time. All three inputs must use the same degree convention; do not supply radians. Longitude and time zone are not inputs because this calculator assumes that declination and local solar hour angle have already been determined. If starting from a date, clock time, and longitude, calculate those astronomical quantities first before using this focused spherical-trigonometry step.

Understand the angle and compass result

The result uses the navigation-style azimuth convention: zero degrees is true north, ninety degrees is east, one hundred eighty degrees is south, and two hundred seventy degrees is west. Values increase clockwise and remain below three hundred sixty degrees. Alongside the numeric angle, the calculator assigns the closest of sixteen compass points, such as NNE, SE, or WNW. Each compass sector spans twenty-two and a half degrees, so the label is a readable summary rather than a replacement for the more precise numeric value. The calculation forms the sun's local east and north vector components from latitude, declination, and hour angle, then applies a quadrant-aware arctangent. That approach avoids the north-versus-south ambiguity that can arise when azimuth is recovered from an inverse cosine alone. The bearing is relative to true north, not magnetic north. A field compass can therefore disagree unless local magnetic declination is applied separately. The output describes direction even if the modeled sun is below the horizon.

Recognize limits and singular positions

Solar azimuth is meaningful when the sun's direction has a horizontal component. If the supplied geometry places the sun exactly at the zenith, directly overhead, every horizontal direction points away from the same position and no unique azimuth exists. The same mathematical ambiguity occurs at the nadir, directly below the observer. The calculator rejects those singular cases instead of returning an arbitrary bearing. Very close to either singularity, small changes in an input can cause a large change in azimuth; that sensitivity is a property of the geometry, not numerical randomness. The calculation also does not correct for atmospheric refraction, terrain, building obstructions, magnetic declination, or the apparent radius of the solar disk. Those effects matter for observed sunrise, sunset, and shading boundaries. For engineering work, retain the numeric bearing and document how declination and hour angle were obtained. Repeating the same input produces the same result, which makes the calculator useful in test fixtures, spreadsheets, scripts, and reproducible solar-position workflows through the API at $0.002 per request.