The Mesoamerican Long Count calendar is a non-repeating, vigesimal (base-20) and base-18 calendar used by several pre-Columbian Mesoamerican cultures, most notably the Maya. For this reason, it is sometimes known as the Maya (or Mayan) Long Count calendar. Using a modified vigesimal tally, the Long Count calendar identifies a day by counting the number of days passed since a mythical creation date that corresponds to August 11, 3114 BCE in the Gregorian calendar. The Long Count calendar was widely used on monuments.
Among other calendars devised in pre-Columbian Mesoamerica, two of the most widely used were the 365-day solar calendar (the Maya version is known as the Haab') and the 260-day calendar, with 20 periods of 13 days. In Mayan studies this 260-day calendar is known as the Tzolk'in, the equivalent Aztec calendar is known by a Nahuatl name, tonalpohualli.
The Haab' and the Tzolk'in calendars identified and named the days, but not the years. The combination of a Haab' date and a Tzolk'in date identifies a specific date in a combination which did not occur again for 52 years. The two calendars based on 365 days and 260 days repeat every 52 Haab' years, a period generally known as the Calendar Round. To designate dates over periods longer than 52 years, some Mesoamericans utilized the Long Count calendar.
The Long Count calendar identifies a date by counting the number of days from a starting date that is generally calculated to be August 11, 3114 BCE in the proleptic Gregorian calendar or September 6 in the Julian calendar (or −3113 in astronomical year numbering). There has been much debate over the precise correlation between the Western calendars and the Long Count calendars. The August 11 date is based on the GMT correlation (see Correlations between Western calendars and the Long Count calendar section elsewhere in this article for details on correlations).
The completion of 13 b'ak'tuns (August 11, 3114 BCE) marks the Creation of the world of human beings according to the Maya. On this day, Raised-up-Sky-Lord caused three stones to be set by associated gods at Lying-Down-Sky, First-Three-Stone-Place. Because the sky still lay on the primordial sea, it was black. The setting of the three stones centered the cosmos which allowed the sky to be raised, revealing the sun.
Rather than using a base-10 scheme, like Western numbering, the Long Count days were tallied in a base-20 and base-18 scheme. Thus 0.0.0.1.5 is equal to 25, and 0.0.0.2.0 is equal to 40. The Long Count is not consistently base-20, however, since the second digit from the right rolls over to zero when it reaches 18. Thus 0.0.1.0.0 does not represent 400 days, but rather only 360 days.
The following table shows the period equivalents as well as Maya names for these periods:
|Representation||Long Count subdivisions||Days||~ solar years|
|0.0.0.1.0||1 winal = 20 k'in||20||0.055|
|0.0.1.0.0||1 tun = 18 winal||360||0.986|
|0.1.0.0.0||1 k'atun = 20 tun||7,200||19.71|
|18.104.22.168.0||1 b'ak'tun = 20 k'atun||144,000||394.3|
Note that the name b'ak'tun is a back-formation invented by scholars. The numbered Long Count was no longer in use by the time the Spanish arrived in the Yucatan peninsula, although unnumbered k'atuns and tuns were still in use.
Long Count dates are written with Mesoamerican numerals, as shown on this table. A dot represents 1 while a bar equals 5. The shell glyph was used to represent the zero concept. The Long Count calendar required the use of zero as a place-holder, and presents one of the earliest uses of the zero concept in history.
The Long Count dates are written vertically, with the higher periods (i.e. b'ak'tun) on the top and then the number of each successively smaller order periods until the number of days (k'in) are listed. As can be seen at left, the Long Count date shown on Stela C at Tres Zapotes is 22.214.171.124.18.
|7||× 144000||= 1,008,000 days (k'in)|
|16||× 7200||= 115,200 days (k'in)|
|6||× 360||= 2,160 days (k'in)|
|16||× 20||= 320 days (k'in)|
|18||× 1||= 18 days (k'in)|
|Total days||= 1,125,698 days (k'in)|
The date on Stela C, then, is 1,125,698 days from August 11, 3114 BCE, Julian day number 1,709,981, September 1, 32 BCE in the proleptic Gregorian calendar, September 3, −31 in the Julian calendar with astronomical year numbering.
On Maya monuments, the Long Count syntax is more complex. The date sequence is given once, at the beginning of the inscription, and opens with the so-called ISIG (Introductory Series Initial Glyph) which reads tzik-a(h) hab’ [patron of Haab' month] ("revered was the year-count with the patron [of the month]"). Next come the 5 digits of the Long Count, followed by the tzolk'in date written as single glyph, and then by supplementary information. Most of this supplementary series is optional and has been shown to be related to lunar data, for example, the age of the moon on the day and the calculated length of current lunation. The date is concluded by a glyph stating the day and month of the Haab year. The text then continues with whatever activity occurred on that date.
A drawing of a full Maya Long Count inscription is shown below.
The earliest Long Count inscription yet discovered is on Stela 2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36 BCE. This table lists the six artifacts with the eight oldest Long Count dates.
|Archaeological site||Name||Gregorian date
(based on August 11)
|Long Count digits||Location|
|Chiapa de Corzo||Stela 2||December 10, 36 BCE||126.96.36.199.13||Chiapas, Mexico|
|Tres Zapotes||Stela C||September 3, 32 BCE||188.8.131.52.18||Veracruz, Mexico|
|El Baúl||Stela 1||March 6, 37 CE||184.108.40.206.12||Guatemala|
|Abaj Takalik||Stela 5||May 20, 103 CE||220.127.116.11.15||"|
|"||"||June 6, 126 CE||18.104.22.168.11||"|
|La Mojarra||Stela 1||July 14, 156 CE||22.214.171.124.7||Veracruz, Mexico|
|"||"||May 22, 143 CE||126.96.36.199.5||"|
|Near La Mojarra||Tuxtla Statuette||March 15, 162 CE||188.8.131.52.17||"|
Of the six sites, three are on the western edge of the Maya homeland and three are several hundred kilometers further west, leading most researchers to believe that the Long Count calendar predates the Maya. La Mojarra Stela 1, the Tuxtla Statuette, Tres Zapotes Stela C, and Chiapa Stela 2 are all inscribed in an Epi-Olmec, not Maya, style. El Baúl Stela 2, on the other hand, was created in the Izapan style. The first unequivocally Maya artifact is Stela 29 from Tikal, with the Long Count date of 292 CE (184.108.40.206.15), more than 300 years after Stela 2 from Chiapa de Corzo.
There have been various methods proposed to allow us to convert from a Long Count date to a Western calendar date. These methods, or correlations, are generally based on dates from the Spanish conquest, when Western dates and unnumbered k'atuns and tuns (positions within the Long Count) are known with some accuracy.
The Maya and western calendars are correlated by using a Julian day number of the starting date of the current creation — 220.127.116.11.0 4 Ajaw, 8 Kumk'u. This is referred to as a correlation constant. The generally accepted correlation constant is the "Goodman, Martinez, Thompson" — GMT correlation of 584,283 days. Using the GMT correlation the current creation started on September 11, 3114 BC (Julian). The study of correlating the Maya and western calendar is referred to as the correlation question.
Michael Coe writes in Breaking the Maya Code that a huge amount of ink has been spilled in the debate over which correlation is the correct one but there can be little doubt that the GMT correlation is correct. The evidence for the GMT correlation is historical, astronomical and archaeological:
Historical: Calendar Round dates with a corresponding Julian date are recorded in Diego de Landa's Relación de las cosas de Yucatán, the Chronicle of Oxcutzkab and the books of Chilam Balam. Oxcutzkab records a date that is a Tun ending. These support the GMT correlation. The fall of the Aztec Empire, Tenochtitlan, occurred on August 13, 1521. A number of different chroniclers wrote that this was a Tzolk'in (Tonalpohualli) of 1 Snake. Various post-conquest scholars such as Sahagun record Aztec_Calendar dates with a calendar date. A number of modern groups in the Guatemalan highlands have continued to keep the Tzolk'in to this day. All of these are consistent with each other, the fall of Tenochtitlan and the GMT correlation.
Astronomical: Any correct correlation must match the astronomical content of classic inscriptions. The GMT correlation does an excellent job of matching lunar data in the supplementary series for example: An inscription at the Temple of the Sun at Palenque records that on Long Count 18.104.22.168.8 there were 26 days completed in a 30 day lunation. The Dresden Codex contains an eclipse table which gives eclipse seasons when the Moon is near its ascending or descending node and an eclipse is likely to occur. Dates converted using the GMT correlation fall roughly in this eclipse season. The Dresden Codex contains a Venus table which records the heliacal risings of Venus. The GMT correlation agrees with these to within a few days which is as accurately as these could have been observed by the ancient Maya.
Archaeological: Various items that can be associated with specific Long Count dates have been isotope dated. In 1959 the University of Pennsylvania carbon dated samples from ten wood lintels from Tikal. These were carved with a date equivalent to 741 AD using the GMT correlation. The average carbon date was 746 +/- 34 years.
If a proposed correlation only has to agree with one of these lines of evidence there could be numerous other possibilities. Astronomers have proposed many correlations for example: Lounsbury, Fuls, et. al. and Bohm and Bohm.
Today, 16:40, Saturday January 16, 2010 (UTC), in the Long Count is 22.214.171.124.10 (GMT correlation).
|Modified Thompson 1||584,284|
|Fuls, et. al.||660,208|
|Long Count||Gregorian date
GMT (584283) correlation
|126.96.36.199.0||August 11, 3114 BCE|
|188.8.131.52.0||November 13, 2720 BCE|
|184.108.40.206.0||February 16, 2325 BCE|
|220.127.116.11.0||May 21, 1931 BCE|
|18.104.22.168.0||August 23, 1537 BCE|
|22.214.171.124.0||November 26, 1143 BCE|
|126.96.36.199.0||February 28, 748 BCE|
|188.8.131.52.0||June 3, 354 BCE|
|184.108.40.206.0||September 5, 41 CE|
|220.127.116.11.0||December 9, 435|
|10.0.0.0.0||March 13, 830|
|18.104.22.168.0||June 15, 1224|
|22.214.171.124.0||September 18, 1618|
|126.96.36.199.0||December 21, 2012|
|188.8.131.52.0||March 26, 2407|
|184.108.40.206.0||June 28, 2801|
|220.127.116.11.0||October 1, 3195|
|18.104.22.168.0||January 3, 3590|
|22.214.171.124.0||April 7, 3984|
|126.96.36.199.0||July 11, 4378|
|188.8.131.52.0.0||October 13, 4772|
According to the Popol Vuh, a book compiling details of creation accounts known to the K'iche' Maya of the Colonial-era highlands, we are living in the fourth world. The Popol Vuh describes the first three creations that the gods failed in making and the creation of the successful fourth world where men were placed. In the Maya Long Count, the previous creation ended at the start of a 14th b'ak'tun.
The previous creation ended on a long count of 184.108.40.206.19. Another 220.127.116.11.19 will occur on December 20, 2012, followed by the start of the fourteenth b'ak'tun, 18.104.22.168.0, on December 21, 2012. There is only one reference to the current creation's 13th b'ak'tun in the fragmentary Mayan corpus: Tortuguero Monument 6, part of a ruler's inscription.
Maya inscriptions occasionally reference future predicted events or commemorations that would occur on dates that lie beyond 2012 (that is, beyond the completion of the 13th b'ak'tun of the current era). Most of these are in the form of "distance dates" where some Long Count date is given, together with a Distance Number that is to be added to the Long Count date to arrive at this future date.
For example, on the west panel at the Temple of Inscriptions in Palenque, a section of the text projects into the future to the 80th Calendar Round (CR) 'anniversary' of the famous Palenque ruler K'inich Janaab' Pakal's accession to the throne (Pakal's accession occurred on a Calendar Round date 5 Lamat 1 Mol, at Long Count 22.214.171.124.8 equivalent to 27 July 615 CE). It does this by commencing with Pakal's birthdate 126.96.36.199.0 8 Ajaw 13 Pop (24 March 603 CE) and adding to it the Distance Number 10.11.10.5.8. This calculation arrives at the 80th Calendar Round since his accession, a day that also has a CR date of 5 Lamat 1 Mol, but which lies over 4,000 years in the future from Pakal's time—the day 21 October in the year 4772. The inscription notes that this day would fall eight days after the completion of the 1st piktun [since the creation or zero date of the Long Count system], where the piktun is the next-highest order above the b'ak'tun in the Long Count. If the completion date of that piktun—13 October 4772—were to be written out in Long Count notation, it could be represented as 188.8.131.52.0.0. The 80th CR anniversary date, eight days later, would be 184.108.40.206.0.8 5 Lamat 1 Mol.
Despite the publicity generated by the 2012 date, Susan Milbrath, curator of Latin American Art and Archaeology at the Florida Museum of Natural History, stated that "We [the archaeological community] have no record or knowledge that [the Maya] would think the world would come to an end" in 2012. "For the ancient Maya, it was a huge celebration to make it to the end of a whole cycle," says Sandra Noble, executive director of the Foundation for the Advancement of Mesoamerican Studies in Crystal River, Florida. To render December 21, 2012, as a doomsday event or moment of cosmic shifting, she says, is "a complete fabrication and a chance for a lot of people to cash in." "There will be another cycle," says E. Wyllys Andrews V, director of the Tulane University Middle American Research Institute (MARI). "We know the Maya thought there was one before this, and that implies they were comfortable with the idea of another one after this." 
As stated, a full Long Count date not only includes the five digits of the Long Count, but the 2-character Tzolk'in and the two-character Haab' dates as well. The five digit Long Count can therefore be confirmed with the other four characters (the "calendar round date").
Taking as an example a Calendar Round date of 220.127.116.11.16 (Long Count) 5 Kib' (Tzolk'in) 14 Yaxk'in (Haab'). One can check whether this date is correct by the following calculation.
It is perhaps easier to find out how many days there are since 4 Ajaw 8 Kumk'u, and show how the date 5 Kib' 14 Yaxk'in is derived.
|9||× 144000||= 1296000|
|12||× 7200||= 86400|
|2||× 360||= 720|
|0||× 20||= 0|
|16||× 1||= 16|
|Total days||= 1383136|
The Tzolk'in date is counted forward from 4 Ajaw. To calculate the numerical portion of the Tzolk'in date, we must add 4 to the total number of days given by the date, and then divide total number of days by 13.
This means that 106395 whole 13 day cycles have been completed, and the numerical portion of the Tzolk'in date is 5.
To calculate the day, we divide the total number of days in the long count by 20 since there are twenty day names.
This means 16 day names must be counted from Ajaw. This gives Kib'. Therefore, the Tzolk'in date is 5 Kib'.
The Haab' date 8 Kumk'u is the ninth day of the eighteenth month. Since there are twenty days per month, there are eleven days remaining in Kumk'u. The nineteenth and last month of the Haab' year contains only five days, thus, there are sixteen days until the end of the Haab' year.
If we subtract 16 days from the total, we can then find how many complete Haab' years are contained.
Dividing by 365, we have
Therefore, 3789 complete Haab' have passed, with 135 days into the new Haab'.
We then find which month the day is in. Dividing the remainder 135 days by 20, we have six complete months, plus 15 remainder days. So, the date in the Haab' lies in the seventh month, which is Yaxk'in. The fifteenth day of Yaxk'in is 14, thus the Haab' date is 14 Yaxk'in.
So the date of the long count date 18.104.22.168.16 5 Kib' 14 Yaxk'in is confirmed.
As mentioned in the Syntax section, there are also four rarely used higher-order periods above the b'ak'tun: piktun, kalabtun, k'inchiltun, and alautun. All of these words are inventions of Mayanists.
It is a matter of dispute whether the first piktun occurs after 13 or after 20 b'ak'tun. In the same way, the fact that a 13-katun cycle was used, didn't negate the fact that there are 20 katuns in a b'ak'tun.
The inscription on Quirigua stela F, or 6, shows a Long Count date of 22.214.171.124.0 1 Ahau 3 Zip (March 15, 761 Gregorian). The huge distance date of 126.96.36.199.188.8.131.52.0 is subtracted and the resulting date is given as (18.)184.108.40.206.0.0.0.0 1 Ahau 13 Yaxkin, which is equivalent to a day over 90 million years in the past. However, there is another distance date on Quirigua Stela D or 4, that gives a date of 220.127.116.11.0 7 Ahau 18 Pop (February 17, 766 Gregorian), to which is added 18.104.22.168.22.214.171.124.0, to give a date of (13.)126.96.36.199.0.0.0.0. This is over 400 million years after the date the stela was erected. It was by calculating a number of these distance dates that Eric Thompson was able to determine that the date of creation in 3114 BCE – 188.8.131.52.0 was actually 0.1.13.0.0.0.0.0.0 in the extended version.
At Yaxchilan, on a temple stairway, there is an inscription that includes four levels above the alautuns. The inscription reads: 184.108.40.206.220.127.116.11.18.104.22.168.9 3 Muluc 17 Mac. This is equivalent to October 19, 744, but the higher cycles do not conform to Thompson’s calculation. The same applies to a Late Classic monument from Coba, Stela 1. The date of creation is expressed as 22.214.171.124.126.96.36.199.188.8.131.52.184.108.40.206.220.127.116.11.0.0.0.0, where the units are 13s in the nineteen places larger than the b'ak'tun.