Calculate Sunlight Hours

The duration of sunlight follows a simple harmonic motion. It is periodic and repeats every year.

In the Northern Hemisphere, the longest day is June 21, and the shortest is December 21. The average
length of daylight is 12 h, and the variation from this average depends on the latitude. (For
example, Fairbanks, Alaska, experiences more than 20 h of daylight on the longest day and
less than 4 h on the shortest day!)

The number of hours of daylight can be modelled by a simple harmonic motion. The following equation models this variation quite well:

Day Hours = a sin(w(t-80))+ 12

a is the half the difference in hours between the longest and shortest day light hours, w is the angular velocity and it equals 2PI/365, t is the number of the day in the year. for example 1st January is one. 31st December is 365 and 21 March is 80 and so on.

For more accurate calculations we need to calculate the hour angle. The following web App gets you the number of day light hours for any place on earth according to the latitude:

Day Length

Day Light Hours

Day :
Month :
year :

Hour :
Minute :
Second :
Time Zone :
Latitude :

Light duration

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