From the makers of DayTime:

Imagine you are facing south, with the position of the sun marking the current time. Day and night are shown by the light and dark regions above and below. (24-hour day or night appear all light or all dark—try it by choosing Vadsø NO, or the US Amundsen-Scott South Pole Station!) Sunrise and sunset positions are marked where night meets day, and the amount of daylight remaining is the arc from the sun’s position to the sunset line (arrow).

For example, at 2:00PM on January 1st in Copenhagen, there were less than 2 hours left of daylight—but without computation one can intuitively see very quickly that the short winter day is almost over.

You can download DayTime from the App Store.