In a horizontal sundial, the angle of the gnomon (the brown triangle) is equal to the latitude . For a given latitude , the distribution of the hour-labeled lines is invariant whatever the day of the year; however, sunrise and sunset times change during the year, due to the change in declination.[more]
The sundial is oriented toward North in the Northern Hemisphere and toward South in the Southern Hemisphere.
Enter any location (latitude °, longitude °), its standard time zone, the Daylight Saving Time (DST), the date, and solar time (in blue). The result is the shadow angle , the shadow cast for a 10 cm high vertical pole, the sun altitude and azimuth , declination , sunrise and sunset times, length of day, and local time (in red).
With the knowledge of your latitude and longitude , you can build a sundial for your location, using the layout of the hour lines, instead of the 3D or 2D sundial settings.[less]
For simplicity, in this Demonstration, sunset and sunrise correspond to a sun altitude , instead of the conventional 50 arc minutes below a horizontal plane.
Latitude is positive in the northern hemisphere and negative in the southern hemisphere.
East longitude is positive and West longitude is negative.
Examples of time zones: Paris, France , New York -.
Latitudes are limited to be below the Arctic circle and above the Antarctic circle; .
For DST seeDaylight Saving Time
The solar altitude angle is the angle between the direction of the sun and a horizontal plane.
The solar azimuth angle is the angle (measured clockwise on the horizontal plane) from the north-pointing coordinate axis to the projection of the Sun's central ray.
For the definitions of solar altitude angle (α), azimuth angle (A) and declination δ 1
The shadow angle is the angle between the noon line and the shadow cast by the tip of the gnomon.
Snapshot 1: 3D view of the sundial in Paris (latitude , longitude ) on June 29, 2012, standard time zone +1, Daylight Saving Time. The length of day is 15h 55' and the sun altitude is 55° 8' at 10:00 (solar time).
Snapshot 2: Sundial in Oslo (latitude , longitude ) on June 29, 2012, standard time zone +1, Daylight Saving Time. The length of day is 18h 22', which is 2h 27' more than in Paris on the same date.
Snapshot 3: Sundial in Paris (latitude , longitude ) on December 21, 2012, standard time zone +1, no DST. The length of day is only 8h 2' and the sun altitude is 16° 28' at 11:00 solar time. Even at 11:00 (solar time), the shadow cast is long (33.8 cm for a 10 cm high vertical pole)
Snapshot 4: Sundial in Rio de Janeiro (latitude , longitude ) on December 15, 2012 (summer in the southern hemisphere), standard time zone , no DST. The length of day is 13h 24' and the sun altitude is 62° 28' at 10:00 (solar time). The sundial is oriented toward the South.
Snapshot 5: Layout for a sundial in Rio de Janeiro (latitude , longitude ) on December 15, 2012 (summer in the southern hemisphere), standard time zone , no DST. The length of day is 13h 24' and the sun altitude is 62° 28' at 10:00 (solar time). The sundial is oriented toward the South.
In Rio, as the date changes from January to December, the day is longest on December 21 and shortest on June 21. The hour lines remain the same (same shadow angles along the year (except for sunrise and sunset) but they are less in winter than in summer.
Try these dates (all approximate):
Vernal equinox, March 21 (day time and night time are equal)
Summer solstice, June 21 (longest day)
Autumnal equinox, September 23 (day time and night time are equal)
Winter solstice, December 21 (shortest day)
Compare the length of day for June 6 (D-Day 1944) and June 21 (the longest day of the year in the northern hemisphere).
You can find geographic coordinates there:
You may compare with these sundial calculators:
Or the U.S. Naval Observatory
W. B. Stine, M. Geyer, and S. R. Stine, Power from the Sun, Chap. 3, "The Sun's Position," 2010. www.powerfromthesun.net/Book/chapter03/chapter03.html#Equation%20of%20Time.
 The Sun's Motion