Maya Civilization

The Long Count and the Calendar Round

The Long Count is the strictly cumulative day-count of the Maya, the framework that placed every day of the Late Preclassic, the Classic, and the early Postclassic inside a single numerical sequence of days counted forward from a zero date 4 Ajaw 8 Kumk’u. The Calendar Round is the smaller cycle of 18,980 days = 73 Tzolkin × 52 Haab’, the period after which a given combined Tzolkin-Haab’ position recurs. Together, the Long Count and the Calendar Round are the two principal means by which a Classic-period date was specified, and almost every surviving monumental inscription carries both.

This page describes the mathematics of the Long Count, the way the Long Count is written in the inscriptions, the major recorded Long Count positions (9.0.0.0.0, 10.0.0.0.0, 11.0.0.0.0, 12.0.0.0.0, 13.0.0.0.0), the structure of the 18,980-day Calendar Round, the way the two were combined in practice, and the modern debate over the correlation constant that links the Long Count to the Gregorian calendar.

The five places of the Long Count

The Long Count is a base-20 number with one structural exception. A typical date is written as baktun.katun.tun.uinal.kin — five place-values, read from largest to smallest:

PlaceNameDaysApprox. solar years
1baktun144,000394.3
2katun7,20019.71
3tun3600.986
4uinal200.055
5kin1—

Each unit is built as 20 of the next-lower unit, except for the tun, which is 18 × 20 = 360 days (not 400) so that the uinal aligns with the 20-day Haab’ month. The 18-base tun is the only irregular place in the system, and the regularity resumes at the next level: a katun is 20 tuns, and a baktun is 20 katuns.

A Long Count such as 9.0.0.0.0 therefore means 9 baktuns × 144,000 days = 1,296,000 days. A Long Count such as 13.0.0.0.0 means 13 × 144,000 = 1,872,000 days — 5,125.37 tropical years — the baktun-13 completion of 21 December 2012.

The base date: 4 Ajaw 8 Kumk’u

The Long Count begins, by convention, on the day 0.0.0.0.0, which in the Calendar Round is 4 Ajaw 8 Kumk’u. The combination of a Tzolkin position (4 Ajaw, the fourth appearance of the Ajaw day in the 260-day cycle) and a Haab’ position (8 Kumk’u, the eighth day of the month Kumk’u) specifies a single day in the 18,980-day Calendar Round, and the Long Count begins the count at that day.

4 Ajaw 8 Kumk’u is, in the Popol Vuh creation account, the day on which the present world was set in place after three previous creations had been destroyed. The Long Count is, in effect, a count of days since the creation.

In the most widely used correlation, the Goodman-Martinez-Thompson (GMT) correlation of 584,283, the base date 4 Ajaw 8 Kumk’u falls on 11 or 13 August 3114 BCE in the proleptic Julian calendar. The Spinden correlation of 489,384 places it 260 days later, on 5 February 3113 BCE in the proleptic Gregorian; the modified GMT of 584,285 places it 2 days after the standard GMT. Modern academic consensus, drawn from the lunar tables in the Dresden Codex, strongly favors the GMT correlation.

The Calendar Round

A single Calendar Round day is specified by a Tzolkin position (coefficient + day-sign) and a Haab’ position (coefficient + month). The 18,980-day Calendar Round is the least common multiple of the 260-day Tzolkin and the 365-day Haab’, and it is the smallest time after which a given combined Calendar Round position recurs.

A 4 Ajaw 8 Kumk’u day, for example, will recur 18,980 days later, when the Tzolkin has cycled 73 times (73 × 260 = 18,980) and the Haab’ has cycled 52 times (52 × 365 = 18,980). The 18,980-day period is the 52-year Calendar Round cycle, the basis of the Mesoamerican New Fire ceremony.

In a Classic-period inscription, the Calendar Round is usually written as a Tzolkin position followed by a Haab’ position, e.g., 9 Ik’ 5 Mol. The Long Count, when given, precedes the Calendar Round.

Major recorded Long Count positions

The following Long Count positions are attested in monumental inscriptions, with the corresponding Haab’-Tzolkin position and the approximate Julian (or proleptic Gregorian) date under the GMT correlation:

  • 7.0.0.0.0 — the base of the Late Preclassic; AD 91 (12 Ajaw 18 Sip, sometimes called the “first creation” date).
  • 8.0.0.0.0 — AD 292 (4 Ajaw 13 Yax), the dedication of the earliest Long Count stelae at Tikal and Naranjo.
  • 9.0.0.0.0 — AD 435 (13 Ajaw 18 K’ank’in), the retroactive dating of the foundation of Tikal’s dynasty by the ruler Yax Ehb’ Xook; commemorated retroactively on Stela 9 at Tikal.
  • 9.4.0.0.0 — AD 514, the early Copán dynasty, the reign of K’inich Yax K’uk’ Mo’.
  • 9.8.0.0.0 — AD 593, the dedication of Stela 3 at Piedras Negras.
  • 9.12.0.0.0 — AD 672, the reign of K’inich Janaab’ Pakal at Palenque.
  • 9.14.0.0.0 — AD 711, the dedication of the Temple of the Inscriptions at Palenque.
  • 9.15.0.0.0 — AD 731, the dedication of Stela N at Copán.
  • 9.17.0.0.0 — AD 771, the reign of K’ahk’ Tiliw Chan Yopaat at Quiriguá.
  • 10.0.0.0.0 — AD 830 (5 Ajaw 3 K’ank’in), the close of the 10th baktun, the moment when the southern lowlands began their long collapse.
  • 10.3.0.0.0 — AD 889, the latest Long Count date at Toniná and at the northern lowland sites.
  • 10.4.0.0.0 — AD 909, one of the latest inscribed Long Count dates in the southern Maya lowlands.
  • 11.0.0.0.0 — AD 1224, a Postclassic date preserved in the Books of Chilam Balam (the inscription has not been recovered on a stone monument).
  • 12.0.0.0.0 — AD 1618, a colonial-era katun marker.
  • 13.0.0.0.0 — AD 2012 (21 December, in the GMT correlation), the baktun-13 completion.

The interval between 10.0.0.0.0 and 11.0.0.0.0 is one 144,000-day baktun, or 394.3 solar years; the interval from 9.0.0.0.0 to 10.0.0.0.0 is the same; and so on. The Long Count allows scholars to locate a given inscription to within a single day in the proleptic calendar, which is one of the most striking features of the Maya writing system.

How the Long Count is written

The Long Count is written in the inscriptions as a sequence of bar-and-dot numerals attached to period glyphs. A bar represents 5, a dot represents 1, and a shell glyph represents 0. A typical Long Count position, 9.12.3.5.8, would be written as:

  • baktun 9: one bar and four dots
  • katun 12: two bars and two dots
  • tun 3: three dots
  • uinal 5: one bar
  • kin 8: one bar and three dots

The bar-and-dot numerals are the basis of Maya mathematics, and the Maya concept of zero (the shell glyph) is used pervasively in Long Count positions such as 10.0.0.0.0, 11.0.0.0.0, 12.0.0.0.0, and 13.0.0.0.0.

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

The Calendar Round in the inscriptions

The Calendar Round is the calendar of ritual and seasonal life. A typical inscription reads:

9.14.13.4.17 12 Kaban 5 Kayab

This is the 9-baktun-14-katun-13-tun-4-uinal-17-kin Long Count, with a Calendar Round position of 12 Kaban 5 Kayab (12 Kaban in the Tzolkin, 5 Kayab in the Haab’). The Long Count places the day at AD 711; the Calendar Round places it in the dry-rain transition month of Kayab; the Tzolkin position places it under the sign of the earth, the earthquake.

The combined format is universal in the Late Classic inscriptions. The same date might also include a “half-Tzolkin” or “k’atun-ending” position, a 260-day count forward or backward, an 819-day count, a 9-day Lords of the Night position, and a lunar series. The full format at Palenque, for example, can include a Long Count, a Calendar Round, a half-Tzolkin, a 9-day Lord, a lunar series, an astronomical event (often a Venus phase), and a historical narrative.

The 52-year cycle and the 18,980-day Calendar Round

The 18,980-day Calendar Round is the basis of the 52-year cycle. A 52-year period in the Haab’ is 52 × 365 = 18,980 days; the same 18,980 days is 73 × 260 = 18,980 Tzolkin cycles. The two cycles return to the same combined position simultaneously every 18,980 days.

The 18,980-day period is not a “century” in the Western sense, but it is a culturally significant interval. A child born on 0 Pop 4 Ajaw would see the day recur 18,980 days later, when they were 52 Haab’-years old. The closing days of such a 52-year cycle were, in Mesoamerican ritual life, a time of cosmic vulnerability, when the year was at risk of “not turning over” — of failing to renew itself. The Aztec New Fire ceremony of 1507 (and earlier 1455, 1403, etc.) is the best-documented example; the Maya equivalent is preserved in the Chilam Balam books and in modern highland K’iche’ ritual.

The 819-day cycle and the Long Count

The 819-day cycle is a Late Classic-period construct attested in the inscriptions of Caracol and a handful of other sites. The cycle, first decoded by David Stuart and elaborated by John Linden and Victoria Bricker, runs 819 days = 7 × 117 = 9 × 91 = 13 × 63 = 3 × 273. The cycle aligns with the Tzolkin (819 = 3 × 260 + 39), with the 9-day Lords of the Night (819 = 9 × 91 = 9 × 7 × 13), and with the 4-color, 4-direction cardinal cycle. The 819-day period rotates through the four colors (red, white, black, yellow) three times, the four cardinal directions three times, and the 13-day trecena 63 times. The cycle has been called the “calendrical harmonic” of the Late Classic.

The 819-day cycle is rare in the inscriptions. It appears at Caracol in the reign of K’an II (AD 537 to 658), at Naranjo in the late 7th century, and at a handful of other sites. The cycle may have been a regional cult-calendar of the K’an dynasty of Caracol and its allies, with limited diffusion beyond.

The 9.0.0.0.0 base and the baktun-13 base

The choice of 4 Ajaw 8 Kumk’u as the Long Count base is itself a product of Maya cosmology. The Tzolkin position 4 Ajaw is the position of the present creation; the Haab’ position 8 Kumk’u is the closing month of the Haab’ year, the month of the granary. The 0.0.0.0.0 4 Ajaw 8 Kumk’u is the moment when the gods created the world, the moment when the granary of time was filled, and the moment from which all subsequent days are counted.

A baktun-13 completion (13.0.0.0.0) is, in this reckoning, the moment when the 1,872,000-day count of the present world is completed, and the count returns to 0.0.0.0.0 4 Ajaw 8 Kumk’u. The 13-baktun cycle is, in other words, a closed cycle, and the 2012 phenomenon is the moment when the count rolled over to begin a new 13-baktun cycle, not the moment when the world ended.

The role of the 4 Ajaw position

The 4 Ajaw position in the Tzolkin is the most sacred seat in the almanac, and the inscription of a 4 Ajaw day in the Calendar Round is the position of the present creation. The 4 Ajaw position recurs in the 260-day cycle every 260 days, but the combined Calendar Round position 4 Ajaw 8 Kumk’u recurs only every 18,980 days. The 4 Ajaw 8 Kumk’u is the unique combination in the 18,980-day cycle that marks the base date of the Long Count.

In the Classic-period inscriptions, a 4 Ajaw 8 Kumk’u Calendar Round day is a ritual marker; a 4 Ajaw (other Haab’ position) day is a sacred but ordinary day; a Long Count completion of 13.0.0.0.0 on 4 Ajaw 8 Kumk’u is a baktun-13 completion, a major event in the Classic-period ritual calendar.

The Long Count in the post-conquest era

The Long Count fell out of use in the lowland Maya communities after the Spanish conquest, although the Books of Chilam Balam preserve the k’atun names and refer to baktun endings in a post-conquest context. The Books of Chilam Balam record the k’atun that began in 1618 (12 Ajaw, the colonial-era “katun of the book”) and the k’atun of 1697 (10 Ajaw, the “katun of the conquest’s end”). The Long Count is not maintained in these books, but the k’atun names are recorded in the same way as in the Classic period, with the same Tzolkin sequence (13, 11, 9, 7, 5, 3, 1, 12, 10, 8, 6, 4, 2 Ajaw).

The modern Long Count

Since the late twentieth century, a movement has emerged in highland Guatemala to maintain the Long Count as a ritual and civil calendar. The Oxlajuj Ajpop group, the Academia de las Lenguas Mayas de Guatemala, and the Guatemalan government have established a unified Long Count calendar with 13.0.0.0.0 falling on 13 December 2012 (Spinden correlation) or 21 December 2012 (GMT correlation). The “Mayan New Year” is celebrated on this date in the highland communities, and the Long Count is taught in some bilingual schools. The modern practice is a revival rather than a continuation; the Long Count is no longer in continuous use from the pre-conquest period, but it has been restored as a marker of modern Maya identity.

The Long Count and the Maya writing system

The Long Count is the most numerically dense text type in the Maya writing system. The bar-and-dot numerals and the period glyphs (baktun, katun, tun, uinal, kin) are universally attested in monumental inscriptions from the Late Preclassic onward, and the Long Count 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.

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