How to Calculate the Winter Solstice Sun Angle

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During a solstice, which occurs around Dec. 21 and June 21 every year, the Earth's axis is positioned relative to the sun such that one hemisphere is closest to the sun and the other is farthest from the sun. The hemisphere farthest from the sun experiences the winter solstice, with the direct rays of the sun falling 23.5 degrees north of the equator. Calculate the sun angle during the winter solstice for your location by determining your latitude and doing two simple calculations.

    Consult an atlas or a geographical website to find the latitude of your location on Earth. For example, if you live in Cape Canaveral, Fla., your latitude is 28° 24' 21" N, or approximately 28.4 degrees.

    Add 23.5 degrees to your latitude to compensate for the fact that the sun's direct rays fall on one of the tropic lines during the winter solstice: the Tropic of Cancer for the northern hemisphere and the Tropic of Capricorn for the southern hemisphere. For example, if you live in Cape Canaveral, add 23.5 to 28.4 to get 51.9 degrees.

    Subtract this value from 90 degrees to get the angle of elevation from the horizon of the sun during midday on the winter solstice. In the above example, subtract 51.9 from 90 to get 39.1 degrees. This is the angle of elevation of the sun in Cape Canaveral at midday.


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