Solar Altitude Calculator (Sun Elevation and Azimuth)

Compute the Sun altitude and azimuth for any moment from latitude, longitude, date, time and time zone. Also returns declination, hour angle and noon altitude.

Input

Enter latitude, longitude, date, time and time zone to compute the Sun altitude and azimuth at that instant.

Latitude

deg

North positive, south negative (−90 to 90)

Longitude

deg

East positive, west negative (−180 to 180)

Date

Time

Time zone

Offset from UTC in hours (Japan is 9)

Result

Sun altitude

77.194371deg

The Sun is above the horizon

Azimuth (from north)

198.218198 deg

Declination

23.437961 deg

Hour angle

4.331425 deg

Solar noon altitude

77.756761 deg

Altitude is sin h ＝ sin(lat) × sin(dec) ＋ cos(lat) × cos(dec) × cos(hour angle). The value is geometric and excludes atmospheric refraction.

How it works

The Sun position is computed with a standard astronomical algorithm based on the Julian day, equivalent to the NOAA Solar Calculator. The clock time and time zone are converted to Universal Time to obtain the Julian day JD, then the Julian century T from J2000.0 gives the geometric mean longitude, mean anomaly and equation of center, leading to the apparent longitude, declination and equation of time.
The hour angle comes from true solar time. True solar time adds the equation of time and a longitude correction (the difference between the location longitude and the standard meridian, which equals the time zone offset times 15 degrees) to the local clock time. The hour angle is 0 at solar noon and positive in the afternoon.
The altitude h is found from latitude phi, declination delta and hour angle H as sin h ＝ sin phi × sin delta ＋ cos phi × cos delta × cos H, with the horizon at 0 degrees and the zenith at 90 degrees.
Azimuth is measured clockwise from north (east 90, south 180, west 270); the Sun is toward the east in the morning and toward the west in the afternoon. The solar noon altitude is 90 minus the absolute difference between latitude and declination.
All angles are in degrees. Atmospheric refraction, which lifts the apparent Sun near the horizon, is not included, so the geometric altitude can differ by tens of arcminutes from the observed value near sunrise and sunset.
Enter latitude positive for north and negative for south, longitude positive for east and negative for west, and the time zone as the offset from Coordinated Universal Time UTC in hours (Japan is ＋9).

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