Sun position calculator: elevation and azimuth

From the instant, the Sun’s declination δ and the equation of time E are computed (Meeus’s low-precision solar coordinates, as in NOAA’s calculator). True solar time is the UTC time of day + E + 4λ minutes, and the hour angle H is that time ÷ 4 − 180°. Then

cos θ_z = sin φ sin δ + cos φ cos δ cos H gives the zenith angle, the elevation is 90° − θ_z, and the azimuth (clockwise from true north) is found from cos A′ = (sin φ cos θ_z − sin δ) / (cos φ sin θ_z).

NOAA’s refraction correction is added to the elevation: for elevations above 5°, (58.1/tan h − 0.07/tan³ h + 0.000086/tan⁵ h)″; between −0.575° and 5°, (1735 − 518.2h + 103.4h² − 12.79h³ + 0.711h⁴)″; below, −20.774″/tan h.

Worked examples: at 40°N, 105°W on 21 June 2010 at 09:54 in UTC−6, the NOAA spreadsheet gives elevation 47.36178° (47.34693° without refraction) and azimuth 98.30692°, which this page reproduces to the last digit shown. For NREL’s Solar Position Algorithm test case (39.742476°N, 105.1786°W, 17 October 2003, 12:30:30 UTC−7) it gives zenith 50.109° and azimuth 194.343°, within 0.003° of NREL’s 50.11162° and 194.34024°.

Limits

Accuracy is about 0.01° for 1800–2100. Refraction assumes standard pressure and temperature and is uncertain near the horizon. Positions are geocentric to within the Sun’s parallax (under 0.003°). The page opens on the current time and your device’s time zone.

References

• NOAA Global Monitoring Laboratory: Solar Calculator
• NOAA GML: solar calculation details (method, refraction, accuracy)
• Meeus, J. (1998). Astronomical Algorithms, 2nd ed. Willmann-Bell (chapters 7, 12, 22, 25, 28)
• pysunnoaa: port of the NOAA spreadsheet with worked outputs
• Reda, I. & Andreas, A. (2004). Solar Position Algorithm for Solar Radiation Applications. NREL/TP-560-34302