The Maya Long Count System

The Maya developed an intricate calendar method whereby events could be tracked from day to day. This aspect of the Maya calendar was an absolute count of days that started 5123 years ago. We do not know why they used that date to start their calendar. If someone from among their ancestors actually started to count from that date, or if someone else extrapolated into the past to that date, or for other causes, is unknown to us. However, since the Long Count will completely fill the baktun count on December 21, 2012 we cannot neglect the possibility that the Maya understood their calendar to be finished on that date.

This impressive calendar is known as the Long Count system. Each day in the sequence is identified by its Long Count number. Mayan Long Count inscriptions denoted five coefficients in the system (a b'ak'tun-count).

We in the Western world use a base-10 numbering system. The Maya used a a base-20 scheme. The Long Count days were tallied in this system. Like an odometer in an automobile the Maya kept on rolling over their day count. Thus is equal to 25, and is equal to 40. The Long Count is not consistently base-20, however, since the third digit rolls over to zero when it reaches 18. Thus 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 1 k'in 1 1/365 1 winal = 20 k'in 20 0.055 1 tun = 18 winal 360 0.986 1 k'atun = 20 tun 7,200 19.71 1 b'ak'tun = 20 k'atun 144,000 394.3

Even with this immense length of time to work with, inscriptions have shown that the Mayans understood that time progressed well beyond that field of time. Theoretically, the system could be extended to include any point in time simply by adding to the number of higher-order place markers used. However, this never happened in the Maya inscriptions, since sufficient length of time had not passed.

We are now about to meet that deadline.

Correlations Between Western Calendars and the Long Count Calendar

Various methods have been proposed 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, where both Long Count and Western dates are known with some accuracy.

The most commonly accepted correlation is the Goodman-Martinez-Thompson correlation. The GMT correlation establishes that the creation date occurred on September 6, 3114 BC (Julian) or August 11, 3114 BC (Gregorian). This correlation fits the known astronomical, ethnographic, carbon dating, and historical sources.

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. There is no evidence that the August 11, 3114 BC date marks any historical event. (Some calculations make this date August 13, 3114 B.)

Long Count dates are written with Mesoamerican numerals. 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 what may be the earliest uses of the zero concept in human 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. The Long Count date shown on Stela C at Tres Zapotes is

7  b'ak'tun × 144000 = 1,008,000
16  k'atun × 7200 = 115,200
6  tun × 360 = 2,160
16  winal × 20 = 320
18  k'in × 1 = 18
  Total 1,125,698 days

The date on Stela C, then, is 1,125,698 days from the beginning of the count to September 1, 32 BC in the proleptic Gregorian calendar.

The Mayans took the long view of time, and named several more slots beyond the baktun. These were in increasing order the piktun, kalabun, kinchiltun, and alautun. Even when those four additional slots have rolled over (about a billion years from now), you can of course keep adding extra slots as needed, even though they don't have special names. As far as is known each higher count represents a factor of 20 chunks of the slot to its right.

(Debate exists about the baktun value of 13. Does it roll over to zero, or does it go on to 20? Since our civilization is coming to an end we shall never know.)

Evidence for the Long Count calendar

The earliest Long Count inscription yet discovered is on Stela 2 at Chiapa de Corzo, Chiapas, Mexico, showing a date of 36 BC. 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 BC Chiapas, Mexico
Tres Zapotes Stela C September 3, 32 BC Veracruz, Mexico
El Baúl Stela 1 March 6, 37 CE Guatemala
Abaj Takalik Stela 5 May 20, 103 CE      "
     "      " June 6, 126 CE      "
La Mojarra Stela 1 July 14, 156 CE Veracruz, Mexico
     "      " May 22, 143 CE      "
Near La Mojarra Tuxtla Statuette March 15, 162 CE      "

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 with the Epi-Olmec system, not strictly Maya. 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 (, more than 300 years after Stela 2 from Chiapa de Corzo.

I shall now show six of these stelae, in chronological sequence, in order for the reader to see how the counts were given on the stelae.

The back of Stela C from Tres Zapotes, an Olmec archeological site. This is the second oldest Long Count date yet discovered. The numerals translate to September 1, 32 BC (Gregorian). The glyphs surrounding the date are what is thought to be one of the few surviving examples of Epi-Olmec script. La Mojarra Stela 1, showing one of the earliest Long Count dates yet discovered, March 6, 37 BC Gregorian (
Stela 5 from Takal'ik Ab'aj. The latest of the two Long Count dates is, equivalent to a date in 126 AD. The dates are flanked by rulers, probably symbolizing the passing of power from one king to the next. Detail showing three columns of glyphs from a portion of the 2nd century AD La Mojarra Stela 1. The left column gives a Long Count date of, or 156 AD. The two right columns visible are glyphs from the Epi-Olmec script.
Frontal view of the Tuxtla Statuette. The Mesoamerican Long Count calendar date of March 162 AD ( is down the front of the statuette. Chichen Itza Initial Series inscription. This date (glyphs A2, B2, …, A5) is   9 Muluk 7 Sak, equivalent to July 28, 878 AD (Gregorian).

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"). For a discussion of how the Calendar Round date verified the Long Count date see:


Long Count Prediction of the Baktun Fill-Up

Importantly, and highly significant, is the fact that none of the surviving, and known, monumental calendar dates go beyond five places in the count. It would have been extremely easy to add another place, to make these descriptions show six instead of five.

This fact strongly suggests that these people did not expect time to reach the sixth place.

Today, 18:49, Monday October 26, 2009 (UTC), in the Long Count is (GMT correlation).

Long Count on October 26, 2009 12 19 16 14 8
Units in Long Count 20 20 18 20 1
Days in Long Count 144,000 7200 360 20 1
Units Remaining in Long Count to reach Baktun 13 0 0 3 3 12
Days Remaining in Long Count     1080 60 12
Total days left in Long Count to reach Baktun 13: (12 X 1) + (3 X 20) + (3 X 360) = 12 + 60 + 1080 = 1152

Since there are 65 days left in 2009, and 365 X 2 days left in 2010 and 2011 = 730, this makes a total of 795 days. How many days are left in 2012 to reach this odometer turn over to zero? 1152 - 795 = 357 days in 2012. From the end of the year of 366 days, (remember Leap Year in 2012), 366 - 357 = 9 days, equal to Dec 22, 2012.

This calculation has nothing to do with what we think might happen at that time. It is strictly a mathematical calculation.

Although I might differ by a day this is the winter solstice date for 2012.

For a discussion of this problem by an astronomer see: