Sun Angle Calculator

The Sun's apparent position can be described with elevation and azimuth. Solar elevation is the angle of the Sun above the horizon: zero degrees lies on the horizon and 90 degrees is directly overhead. A negative elevation means the calculated Sun position is below the horizon. Solar azimuth gives the compass direction measured clockwise from north, so east is 90 degrees, south is 180 degrees, and west is 270 degrees. This calculator estimates declination with a common day-of-year approximation, then combines declination, latitude, and hour angle using spherical astronomy relationships. Solar declination is the angular position of the Sun north or south of Earth's equatorial plane. It varies from about -23.45 degrees at the December solstice to +23.45 degrees at the June solstice and is near zero at the equinoxes. The hour angle changes by 15 degrees per hour and is zero at local solar noon. Local solar time is not always the same as the clock shown on a phone or wall. Clock time is organized around civil time zones and may include daylight saving time. Solar time also shifts with longitude within a time zone and the equation of time, which reflects Earth's orbital geometry. For precise work, convert civil time to apparent solar time before using this simplified calculator. Enter southern latitudes as negative values and northern latitudes as positive values. Sun-angle estimates support solar-panel orientation, shading studies, daylight planning, photography, agriculture, and educational astronomy. The approximation is useful for quick analysis but omits atmospheric refraction, observer elevation, terrain, and the small year-to-year changes handled by high-precision ephemerides. Refraction is especially important close to the horizon. For navigation, legal sunrise definitions, concentrated solar design, or safety-critical planning, use authoritative astronomical data and location-specific methods. Always check whether an application defines azimuth from north or from south, because both conventions appear in technical references.