The Mayan long count calendar

The Maya named their days with a system of two parallel calendars.  The ritual Tzolk'in used numbers from 1-13 together with a sequence of twenty named days, which repeated in a 260-day cycle.  The civil Haab' consisted of 18 months of 20 days, numbered 0-19, with another period of 5 days added to make a total of 365.  These two calendars together repeated in a 52-year cycle, and could be used to identify any date in what was likely an average lifespan.  But to refer to historical dates in the past and future, the Maya used the long count, which was simply the number of days since the mythical creation date of 11 August 3114 BCE.

The long count is a number consisting of five numerals; but the first, third, and fourth place numerals use base 20, and the second uses base 18.  Sources disagree on whether the fifth actually uses base 13 or 20.  Here is a summary of how a complete date is constructed:

The second place long count digit is base 18 because there are 18, not 20, winal in one tun.  The 360-day tun may have actually been the basis of another calendar system.

The beginning of the current creation cycle, 11 August 3114 BCE, was designated 13.0.0.0.0.  It was followed by 0.0.0.0.1, which implies a long count cycle of 13 b'ak'tun (5125 years).  Other sources, however, describe a unit of one piktun as 20 b'ak'tun, implying that the b'ak'tun should be base 20 like the other units.

The Tzolk'in and Haab' dates of the original 13.0.0.0.0 were 4 Ajaw, 8 Kumk'u; these are the starting points for the rest of the series.  The next day was thus 0.0.0.0.1, 5 Imix', 9 Kumk'u.

As an example of a long count date, Apollo 11 landed on the moon on 12.17.15.17.0, 4 Ajaw, 18 Tzek.  This means that this date was (12 × 144,000) + (17 × 7200) + (15 × 360) + (17 × 20) + (0 × 1) = 1,856,140 days since the creation date.

It may be easier to understand the long count dates by watching how they work.  Here is one 365-day Haab' cycle, with day 366 added to show how the cycle repeats.  Both beginning points of the Tzolk'in and Haab' cycles are highlighted.  Since there are 20 Tzolk'in day names, they correspond to the last (base 20) digit of the long count.  Not all Tzolk'in and Haab' combinations can actually occur.  Note that 12/21/2012, like the original creation date, is the completion of a 13-b'ak'tun cycle.