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Wndsn Sun Calculator

Companion to Wndsn Quadrant Telemeters: Low tech, high utility graphical distance computers from the Wndsn applied science lab.

By way of using a Wndsn Quadrant to measure local latitude and calculate declination for a given date, a number of values can be derived through further Quadrant computations.

The celestial sphere and the navigational triangle.

The celestial sphere and the navigational triangle with all relevant variables.


Enter latitude φ and solar declination δ to compute a variety of Sun data.


The equations are proof-of-concept formulas and ignore specifics like atmospheric refraction, etc. The calculated results are FOR EDUCATIONAL PURPOSES ONLY; some are exact, some are approximate, and some are simplified. Actual Sun data may vary significantly.


  • Latitude φ: 52.5°
  • Date: 2019-01-06
  • Instantaneous Sun altitude h: 10°

General calculations for latitude

  • Maximum solar altitude H on equinoxes for latitude given: 37.5°
  • Maximum solar altitude H on summer solstice for latitude given: 60.94°
  • Maximum solar altitude H on winter solstice for latitude given: 14.06°
  • Summer solstice sunrise αsr and sunset αss azimuth: 49.2° and 310.8°
  • Winter solstice sunrise αsr and sunset αss azimuth: 130.8° and 229.2°

Diurnal calculations for latitude and declination or date

  • Day #: 6
  • Declination δ: -22.49°
  • Sunrise azimuth αsr: 128.93°
  • Sunset azimuth αss: 231.07°
  • Hour angle at sunrise tsr: 57.35°
  • Sun hours: 07:36
  • Length of unequal Sun hour: 38 min
  • Noon altitude H: 15.01°
  • Equation of time: -05:12

Instantaneous calculations for Sun altitude

  • Hour angle t: 31.98°
  • Time to or from noon: 02:04
  • Sun azimuth αs: 136.1°
  • Shadow length (of a stick with a height of 1 unit): 5.67

The display precision set is .2. To change that, edit the variable &digits=x in the URL where 0 <= x <= 9.


[Load sample values (JSON) (XML) (CSV).]

Sun altitude at noon H from latitude:
H = (90° − φ) + δ
Azimuth αsr of rising/setting sun:
cos αsr = sin δ / cos φ
Hour angle tsr of rising/setting sun (from noon):
cos tsr = -tan φ * tan δ
Hour angle t from instantaneous Sun altitude h:
cos t = (sin h - sin δ * sin φ) / (cos δ * cos φ)
Sun azimuth αs for a given hour:
tan αs = (sin t / (sin φ * cos t)) - cos φ * tan δ

where H = Sun altitude at noon, h = instantaneous Sun altitude, t = hour angle, φ = latitude, and δ = declination.

See also