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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.

Calculate range.

The celestial sphere with all relevant variables showing the relationship between the equatorial and azimuthal coordinate system.


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


[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 τsr of rising/setting Sun (from noon):
cos τsr = -tan φ · tan δ [To offset refraction, for true sunrise/set, a constant of 1.66667° is added to the result.]
Hour angle τ from instantaneous Sun altitude h:
cos τ = (sin h - sin δ · sin φ) / (cos δ · cos φ)
Sun azimuth αs for a given hour:
tan αs = sin τ / (sin φ · cos τ - cos φ · tan δ)

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


  • For certain locations, such as Sevilla in Spain, which is located at 6°W but belongs to the "wrong" timezone CET (UTC+1), the results returned may be partially wrong, since Tycho calculates from true longitude only.

See also