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The shortest day of the year is the Winter Solstice; in the northern hemisphere, that's generally December 21. On December 22, the day is longer by a matter of a few seconds, and on December 23, the day is longer by a couple of seconds more. We don't really start to notice the day length changing until mid January.

The length of day follows a sinusoidal pattern, and the day length is increasing fastest around the time of the equinoxes.

The US Naval Observatory has a calculator that can give you the times of sunrise and sunset for an entire year for your location.

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