Solar Angle Calculator

Calculate solar altitude and azimuth angles from latitude, day of year, and solar time.

Geographic latitude in degrees. Positive for Northern Hemisphere, negative for Southern. Ranges from -90 to 90.
degrees
Day number from 1-365 (Jan 1 = 1, Dec 31 = 365). Used to compute solar declination angle throughout the year.
1-365
Local solar time in 24-hour format (e.g., 12 = solar noon, 9 = 9 AM solar time). Solar noon is when the sun is due south (northern hemisphere).
hours (0-24)

Results

Solar Declination-degrees
Hour Angle-degrees
Solar Altitude Angle-degrees
Solar Azimuth Angle-degrees
Solar Zenith Angle-degrees
References:
Solar declination: d = 23.45 * sin(360/365 * (DOY - 81)). Hour angle: HA = (hour - 12) * 15. Altitude: sin(a) = sin(lat)*sin(dec) + cos(lat)*cos(dec)*cos(HA). Azimuth measured from North (0/360=N, 90=E, 180=S, 270=W).