Sun Positions
using simple approximations
by Prof. Richard B. Goldstein of Providence College
Location in degrees:
latitude (°) N(+) / S(-) Equator is 0.0
longitude (°) E(+) / W(-)  London is 0.0

currentuser input
month (1 to 12)
day (1 to 31)
± time from noon (hrs)
Fill in column on right or use the
check box: for current values.


sun declination (°)
1.0=equator at equinox
Sun Position
in new coordinates
on a unit sphere:
azimuth (°)                               altitude (°)

  • In the graphical output the sun's azimuth is shown hourly on the left.  The red line shows the current position and the blue lines show the sunrise and sunset if they occur.
  • The black pie outlined segment on the right shows the extent of the sun's altitude during the full 24 hours from midnight to noon to midnight.  Red indicates it is the day and how high the sun's altitude is currently; likewise, blue indicates it is night and how low the sun's position is below the surface currently.
  • For the diagram on the bottom the sun's hourly positions are shown for winter solstice, equinox, and summer solstice.  The elliptical orbit is in red and the sun solid yellow with a red outline when it is day and the elliptical orbit is in blue and the sun has a blue dot and blue outline when it is night.  The hours of midnight, 6 AM, noon, and 6 PM are shown in solid green.
  • For those interested: Sundial Calculations and Diagram

The following equations were used (derivation):

Some suggested sources:

Commercial sites:
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