``The Mesoamerican calendar, one of the most sophisticated timekeeping systems ever conceived by ancient people.'' -- Anthony F. Aveni, Skywatchers of Ancient Mexico
Extensive evidence shows that Prehispanic Mexicans have, from immemorial time and obtained as a result of prolonged astronomical and meteorologic observations, calendrical systems to measure the passage of time.
These calendars had enormous importance, in daily life, in ceremonies and festivals, in the agriculture, and in the complexity of their religious thought and cosmovision.
Two were basically the calendrical systems from where other chronological calculations were developed in a precise and complex manner. One was the civil or solar calendar, of 365 days, made up of 18 sets of twenty days ("veintenas") plus 5 more days at the end. Throughout those 365 days another calendar system provided names to those days based on an astrological and ritual basis in cycles of 260 days. In this calendar, there were 4 divisions of 65 days, each subdivided in 5 periods of 14 days ("trecenas").
The count of days and destines were carried out by means of numerals, from 1 to 13, that in combination with 20 day signs formed a unique sequence of 260 days. In order to indicate a date with precision it was necessary to represent the combination of numeral and day sign, and also the name of the month or veintena.
In addition, as a consequence of the introduction of the extra five days at the end of the solar year, only 4 day signs could be the markers or year bearers, i.e., the day signs of the day that would name the year. Among the Mexica, these 4 day signs were Acatl (Reed), Tecpatl (Flint), Calli (House), Tochtli (Rabbit). Combining again those 4 day signs with the numerals from 1 to 13 results in 52 years, the so called Binding of the Years, whose end was observed in special ceremonies to kindle a "New Fire".
Among the Olmec and the Maya another chronological measure was in use, the Long Count represents a count of days from a distant origin.
The following sections presents a more detail discussion of the Maya and Mexica calendars, including a calculator to convert dates below:
12. 18. 17. 16. 6. 6-Cimi 19 Kayab / / / / / \ \ \ \ Batkun = 20 K/ / / / / \ \ \ \__ Month  / / / / \ \ \ Katun = 20 Tun_/ / / / \ \ \____ Day (0-19) / / / \ \ Tun = 18 Uinals__/ / / \ \_______ Sign  / / \ Uinal = 20 kins____/ / \__________ Numeral (1-13) / \--v--/ \---v---/ kin = 1 day_________/ Tzolkin Haab \------v------/ ^--Baktun Count----^ Calendar Round
Long Count or initial series counts the number of days since creation, Aug 12, 3113 B.C. (according to the GMT or Goodman-Martinez-Thompson correlation.)
Batkun count (days) = (((B*20 + K)*20 + T)*18 + U)*20 + kins = 144000*B + 7200*K + 360*T + 20*U + kinsThe Mayan Calendar Round is composed of the Tzolkin and the Haab. The Tzolkin is the name given to the period of 13x20 = 260 days and includes a numeral (1-13) and one of twenty signs (names).
The Haab is a civil year of 19 months, 18 of them with 20 days numbered from 0 to 19, and the last month with 5 days numbered 0 to 4. The months of the Haab are listed in Table 1.
|Uo||Frog||Atlcahualco||Departure of the waters|
|Zip||Stag||Tlacaxipehualiztli||Flaying of men|
|Yaxkin||Tender sun (green)||Etzalcualiztli||Meal of Corn and Bean|
|Mol||Reunion||Tecuilhuitontli||Little Feast of Lords|
|Chen||Well||Hueytecuilhuitl||Grand Feast of Lords|
|Yax||Green||Miccailhuitontli||Little Feast of The Dead|
|Zac||White||Hueymiccailhuitl||Grand Feast of The Dead|
|Kankin||Mature sun (yellow)||Hueypachtli||Large Hay|
|Pax||Music||Panquetzaliztli||Raising of the Banners|
|Kayab||Turtle||Atemoztli||Lowering of water|
The names of the Mexica months and their meanings are also listed in table 1. It is worthy to note that the Maya and Nahuas began their New Year at different times, and hence the months do not correspond as listed.
Xihuitl: 5-Acatl. Tonal: 6-Miquiztli. Meztli: Tecuilhuitontli 1 | | | | | | | | | Year 1-13 Sign Day 1-13 Sign Month Name  Day#
The Aztec (also known as Mexica or Nahua) calendar is derived from the Maya but excludes the long count and adds a year name which is also formed with a numeral (1-13) and 1 of 4 signs in a cycle of 52 years (Xiuhmolpilli). The 260- day period is known as Tonalpohualli and the 365-day year as Xiuhuitl. The correlation with the Gregorian calendar is due to Alfonso Caso. 
The signs of the days are in Table 2. The column indicated by the label ``Order'' represents the name of that numeral. For instance, in Nahuatl, Ce is 1, Ome is 2, and so on.
|Mi (0)||Imix||Ce (1)||Cipactli||Crocodile|
|Hun (1)||Ik||Ome (2)||Ehecatl||Wind|
The glyphs for each day sign can be counted counterclockwise from the top
on the third ring of the Aztec sunstone.
The Tarascans or Purepecha had a similar calendar as the Az- tecs, but started the year on different days. The Zapotecs are believed to have invented the Mesoamerican ritual calen- dar of 260 days. Their calendar then presents 4 subdivisions of that period of 65 days (Cocijo) with smaller subdivisions of 13 days (Cocij) named according to the name of the first day.
As far as correlation to the Western calendar is concerned, the most common ones are mentioned in the references.