Maya Civilization

How Does the Maya Long Count Calendar Work?

The Long Count is the strictly cumulative day-count of the Maya calendar system. It is the framework in which the Tzolkin and the Haab’ are embedded, and the framework that allows modern epigraphers to locate any Classic-period inscription to within a single day in the proleptic Julian or Gregorian calendar. To read a Long Count date, you need to know the five place-values, the base date 4 Ajaw 8 Kumk’u, the way the places are combined into a single day-count, and the way the day-count is converted to a solar date via the Goodman-Martinez-Thompson (GMT) correlation.

This page describes the structure of the Long Count, the way the place-values are read, the way the Long Count is converted to a Calendar Round, the way the Long Count is converted to a solar date, and the way the Long Count is written in the inscriptions using bar-and-dot numerals and period glyphs.

The five places of the Long Count

A Long Count is written as five place-values, read from largest to smallest:

  • baktun — 144,000 days (20 × 7,200, or roughly 394.3 solar years)
  • katun — 7,200 days (20 × 360, or roughly 19.7 solar years)
  • tun — 360 days (18 × 20, or roughly 1 solar year, minus 5 days)
  • uinal — 20 days (20 × 1)
  • kin — 1 day

The five places multiply to a single integer. A Long Count of 9.12.3.5.8 is, for example, 9 baktuns + 12 katuns + 3 tuns + 5 uinals + 8 kins = 9 × 144,000 + 12 × 7,200 + 3 × 360 + 5 × 20 + 8 = 1,296,000 + 86,400 + 1,080 + 100 + 8 = 1,383,588 days. The total is the number of days elapsed since the base date 4 Ajaw 8 Kumk’u.

The base date is 0.0.0.0.0 4 Ajaw 8 Kumk’u, and every Long Count date is the number of days elapsed since this base. The 9.0.0.0.0 Long Count, for example, is 9 × 144,000 = 1,296,000 days after the base, which corresponds (in the GMT correlation) to AD 435 and the Calendar Round position 13 Ajaw 18 K’ank’in.

The place-values and the base-20 system

The Long Count is a base-20 (vigesimal) system with one structural exception: the tun is 18 × 20 = 360 days, not 20 × 20 = 400 days. The reason for the 18-base tun is that the tun aligns with the 18-month Haab’ year, with 18 × 20 = 360 days making the tun a “Haab’ minus 5” year. The 18-base tun is a useful approximation for the Long Count, and it allows the katun and baktun to be simple multiples of 20.

The place-value system is the basis of the Maya number system and the concept of zero. The Maya were one of the few pre-modern civilizations to develop a true place-value number system with the concept of zero, and the Long Count is the most elaborate application of the system. The bar-and-dot numerals (a bar = 5, a dot = 1) and the shell glyph for zero are the basis of the Long Count inscriptions.

Reading a Long Count date

A Long Count date such as 9.14.13.4.17 is read aloud as “nine baktuns, fourteen katuns, thirteen tuns, four uinals, seventeen kins.” The date is unambiguous and corresponds to a single day in the proleptic calendar. The same date in the Tzolkin is determined by computing the Long Count day mod 260; the same date in the Haab’ is determined by computing the Long Count day mod 365.

The Tzolkin position of a Long Count date can be computed using the formula: Tzolkin coefficient = ((4 × Long Count day) + 1) mod 13; Tzolkin day-sign = (Long Count day + 159) mod 20. The Haab’ position is computed using a separate set of formulas. In practice, epigraphers use conversion tables or software (such as the GMT-correlation programs of the Maya calendar community) to convert Long Count dates to Calendar Round positions.

The base date and the creation

The base date 4 Ajaw 8 Kumk’u is the day on which the present world was created, according to the Maya creation mythology recorded in the Popol Vuh and the Classic-period inscriptions. The 4 Ajaw position in the Tzolkin is the most sacred seat in the 260-day cycle, the day of the Hero Twins’ ascent to the sun and the moon. The 8 Kumk’u position in the Haab’ is the eighth day of the closing month of the year, the month of the granary.

The base date 4 Ajaw 8 Kumk’u is the most sacred day in the Maya calendar. Every Long Count date is the number of days since this day, and the 13-baktun completion 13.0.0.0.0 falls on the same Calendar Round position 4 Ajaw 8 Kumk’u. The 13-baktun cycle is, in other words, a 1,872,000-day cycle that returns to the same Calendar Round position as the base.

The correlation problem

The Long Count is a day-count, but it is not directly tied to the proleptic Julian or Gregorian calendar. The tie is made through a “correlation constant” that maps a Long Count day to a solar date. The most widely used correlation is the Goodman-Martinez-Thompson (GMT) correlation of 584,283, which maps the base date 4 Ajaw 8 Kumk’u to 11 or 13 August 3114 BCE (the 11/13 ambiguity is due to the conversion from the proleptic Julian to the proleptic Gregorian).

The GMT correlation is the modern academic standard. It is supported by the lunar tables in the Dresden Codex, which allow the absolute date of a Long Count position to be reconstructed to within a day. The lunar tables are consistent with the GMT correlation but not with the Spinden correlation of 489,384, which places the base date 260 days later, or with the modified GMT of 584,285, which places it 2 days later.

The correlation problem is one of the most consequential issues in Maya astronomy. The choice between the GMT and the Spinden correlations shifts the absolute dates of all Classic-period inscriptions by 260 days, and the choice between the GMT and the modified GMT shifts them by 2 days. The 21 December 2012 date for the 13-baktun completion, for example, is the GMT date; the Spinden date is 13 December 2012, and the modified GMT date is 23 December 2012.

The 9.0.0.0.0 base and the baktun-9 start (AD 435)

The 9.0.0.0.0 Long Count, equivalent in the GMT correlation to 13.0.0.0.0 + 9 × 144,000 = 1,296,000 days, is dated to AD 435. The 9.0.0.0.0 position is the close of the 9th baktun, the moment when the count advances to 10.0.0.0.0. The position is significant in the Classic-period inscriptions as the retroactive commemoration of the foundation of the Tikal dynasty: the ruler Yax Ehb’ Xook, founder of the dynasty, is recorded in later inscriptions as having taken office at 9.0.0.0.0, even though the dynasty was actually founded several centuries earlier.

The 9.0.0.0.0 position is commemorated on Tikal Stela 9, Quiriguá Stela C, and a number of other monuments. The 9.0.0.0.0 baktun-ending was a major event in the Late Classic period, and the monuments of the period record the king’s role in the cosmic cycle.

The 10.0.0.0.0 baktun-ending (AD 830)

The 10.0.0.0.0 Long Count, equivalent in the GMT correlation to 1,440,000 days, is dated to AD 830. The 10.0.0.0.0 position is the close of the 10th baktun, the moment when the count advances to 11.0.0.0.0. The position is significant in the Terminal Classic period as the moment when the southern lowland cities began their long collapse.

The 10.0.0.0.0 baktun-ending is recorded in the inscriptions of Dos Pilas, Aguateca, Cancuén, and Quiriguá. The monuments of the period document a sharp uptick in warfare, with the Petexbatun wars recorded in the inscriptions of the period. The 10.0.0.0.0 baktun-ending is one of the most carefully documented Long Count positions in the Late Classic record.

The 11.0.0.0.0 baktun-ending (AD 1224) and the 12.0.0.0.0 baktun-ending (AD 1618)

The 11.0.0.0.0 Long Count, equivalent in the GMT correlation to 1,584,000 days, is dated to AD 1224. The position is not recorded in monumental inscriptions, although it is recorded in the colonial-era Books of Chilam Balam. The 11.0.0.0.0 baktun-ending is, in the Chilam Balam, a marker of the Postclassic period, and the k’atun 4 Ajaw prophecy is associated with the period.

The 12.0.0.0.0 Long Count, equivalent to 1,728,000 days, is dated to AD 1618. The position is a colonial-era marker, falling just after the Spanish conquest, and the k’atun 13 Ajaw of this period is recorded in the Books of Chilam Balam as the “katun of the book,” a time of pestilence and the imposition of colonial rule.

The 13.0.0.0.0 baktun-13 completion (AD 2012)

The 13.0.0.0.0 Long Count, equivalent to 1,872,000 days, is dated to 21 December 2012 in the GMT correlation. The position is the close of the 13-baktun cycle, the moment when the count returns to 0.0.0.0.0 4 Ajaw 8 Kumk’u. The 13-baktun completion is the source of the modern “2012” phenomenon, although the actual Maya record does not predict an end of the world at this moment.

The 13-baktun completion is recorded in the Tortuguero Monument 6 inscription and in the Books of Chilam Balam, and it is celebrated in the highland communities of Guatemala as the Mayan New Year. The 13-baktun completion is, in the modern academic record, a cycle rollover, not a cosmic catastrophe.

The bar-and-dot numerals and the period glyphs

The Long Count is written in the inscriptions using bar-and-dot numerals and period glyphs. A bar represents 5, a dot represents 1, and a shell glyph represents 0. The period glyphs are:

  • Baktun glyph — a variant of the ajaw face glyph, with a numerical coefficient attached.
  • Katun glyph — a glyph of a tied bundle, with a numerical coefficient attached.
  • Tun glyph — a glyph of a stone or a k’in face, with a numerical coefficient attached.
  • Uinal glyph — a glyph of a moon or a k’in face, with a numerical coefficient attached.
  • Kin glyph — a k’in face with a numerical coefficient attached.

The period glyphs are universal in the Late Classic inscriptions, and the bar-and-dot system is one of the most compact numerical notations ever developed. The Long Count inscriptions represent the densest numerical record of any pre-modern civilization.

The Long Count and the Maya writing system

The Long Count is the most numerically dense text type in the Maya writing system. The Long Count appears in over 10,000 inscriptions from the Late Preclassic through the Late Classic, and it is the basis of the modern chronology of the Classic Maya. The decipherment of the Long Count by Ernst Förstemann in the late nineteenth century was the first major breakthrough in Maya hieroglyphic decipherment, and the Long Count is now so well-understood that the absolute date of a Classic-period inscription can be determined to within a single day in the proleptic Julian calendar.

The Long Count is also the basis of the modern Maya historical chronology. The Classic-period kings, their accessions, their wars, and their monuments can be placed in absolute chronology using the Long Count, and the chronology is one of the most precise pre-modern chronologies in the world. The Long Count is, in this respect, a “day-clock” of the Maya civilization.

Sources

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