The Mayans employed three calendars, all organised as hierarchies of cycles of days of various lengths. The Long Count was the principal calendar for historical purposes, the Haab was used as the civil calendar, while the Tzolkin was the religious calendar. All of the Mayan calendars are based on serial counting of days without means for synchronising the calendar to the Sun or Moon, although the Long Count and Haab calendars contain cycles of 360 and 365 days, respectively, which are roughly comparable to the solar year. Based purely on counting days, the Long Count more closely resembles the Julian Day system and contemporary computer representations of date and time than other calendars devised in antiquity. Also distinctly modern in appearance is that days and cycles count from zero, not one as in most other calendars, which simplifies the computation of dates, and that numbers as opposed to names were used for all of the cycles.

Cycle	Composed of	Total Days	Years (approx.)
kin		1
uinal	20 kin	20
tun	18 uinal	360	0.986
katun	20 tun	7200	19.7
baktun	20 katun	144,000	394.3
pictun	20 baktun	2,880,000	7,885
calabtun	20 piktun	57,600,000	157,704
kinchiltun	20 calabtun	1,152,000,000	3,154,071
alautun	20 kinchiltun	23,040,000,000	63,081,429

The Long Count calendar is organised into the hierarchy of cycles shown at the right. Each of the cycles is composed of 20 of the next shorter cycle with the exception of the tun, which consists of 18 uinal of 20 days each. This results in a tun of 360 days, which maintains approximate alignment with the solar year over modest intervals--the calendar comes undone from the Sun 5 days every tun.

The Mayans believed at at the conclusion of each pictun cycle of about 7,885 years the universe is destroyed and re-created. Those with apocalyptic inclinations will be relieved to observe that the present cycle will not end until Columbus Day, October 12, 4772 in the Gregorian calendar. Speaking of apocalyptic events, it's amusing to observe that the longest of the cycles in the Mayan calendar, alautun, about 63 million years, is comparable to the 65 million years since the impact which brought down the curtain on the dinosaurs--an impact which occurred near the Yucatan peninsula where, almost an alautun later, the Mayan civilisation flourished. If the universe is going to be destroyed and the end of the current pictun, there's no point in writing dates using the longer cycles, so we dispense with them here.

Dates in the Long Count calendar are written, by convention, as:

baktun . katun . tun . uinal . kin

and thus resemble present-day Internet IP addresses!

For civil purposes the Mayans used the Haab calendar in which the year was divided into 18 named periods of 20 days each, followed by five Uayeb days not considered part of any period. Dates in this calendar are written as a day number (0 to 19 for regular periods and 0 to 4 for the days of Uayeb) followed by the name of the period. This calendar has no concept of year numbers; it simply repeats at the end of the complete 365 day cycle. Consequently, it is not possible, given a date in the Haab calendar, to determine the Long Count or year in other calendars. The 365 day cycle provides better alignment with the solar year than the 360 day tun of the Long Count but, lacking a leap year mechanism, the Haab calendar shifted one day with respect to the seasons about every four years.

The Mayan religion employed the Tzolkin calendar, composed of 20 named periods of 13 days. Unlike the Haab calendar, in which the day numbers increment until the end of the period, at which time the next period name is used and the day count reset to 0, the names and numbers in the Tzolkin calendar advance in parallel. On each successive day, the day number is incremented by 1, being reset to 0 upon reaching 13, and the next in the cycle of twenty names is affixed to it. Since 13 does not evenly divide 20, there are thus a total of 260 day number and period names before the calendar repeats. As with the Haab calendar, cycles are not counted and one cannot, therefore, convert a Tzolkin date into a unique date in other calendars. The 260 day cycle formed the basis for Mayan religious events and has no relation to the solar year or lunar month.

The Mayans frequently specified dates using both the Haab and Tzolkin calendars; dates of this form repeat only every 52 solar years.

Adapted from Formilab's Calendar Converter.