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In modern usage, an hour is defined as a unit of time 60 minutes, or 3600 seconds in length. It is approximately 1/24 of a median Earth day.

Earlier definitions of the hour:

Counting hours

Every definition of the hour came with its own starting point for counting the hours.

This manner of counting hours has the advantage that everyone can easily read the clock to see how much time he will have to finish his daywork without artificial light. It was introduced in Italy during the 14th century and lasted until mid-18th century, in some regions until mid-19th century. It was also used in Poland and Bohemia until the 17th century.
Sunrise and sunset are much more conspicuous points in day than noon or midnight; starting to count then is much easier than starting at noon or midnight. With modern astronomic equipment (and the telegraph or similar means to transfer a time sign in a split-second), this issue is no more relevant.

Sundials often show the hour length and count according to one of the older definitions and countings.

There are probably 12 hours because there are approximately 12 lunar months in a solar year. Symmetries of this sort are common in ancient units of measurement.

See also: canonical hours, times from 1 kilosecond to 10 kiloseconds