The Number System

Modern cultures use a number system based on ten, called the decimal system. In the decimal system, ten symbols (numerals) represent the numbers from 0 to 9. For numbers greater than 9, the position of the numeral represents a multiple of 10. This is demonstrated at right for the number 3027.

The Mayan number system is based on twenty. (This is called a vigesimal system.) Twenty symbols, or glyphs, represent the numbers from 0 to 19, and the position of a glyph represents a multiple of twenty.

The numbers 1 to 19 are usually represented by a group of dots and lines; a dot represents 1, and a line represents 5. In addition, each number can be represented by a face glyph, but I won't deal with that subject here. Various glyphs represent 0, but the shell glyph is the simplest. The table at right shows the numbers from 0 to 19.

The dots and lines of these numbers can be arranged horizontally, or vertically, as shown at left.

The Maya often drew or sculpted little ornaments to fill the spaces around the dots. It is necessary to distinguish between dots which have a numeric value and space fillers. For example, the numbers at right represent 6 and 12. They do not represent 8 and 14.

As mentioned above, the position of a glyph represents a multiple of twenty. The Maya wrote numbers vertically, with the units at the bottom. Above the units were the twenties, above the twenties, the four hundreds (20 x 20), and above the four hundreds, the eight thousands (20 x 20 x 20).


About the Calendar

(There is a short explanation about the pronunciation of Mayan words here. If you wish to read that later, please be aware that the 'x' was pronounced as 'sh'.)

The Mayan calendar is a combination of two calendars, which are called, in the modern Yucatec language, Tzolk'in and Haab. First I'll describe the Tzolk'in.

The Tzolk'in-Calendar

Tzolk'in means 'count of days'. A date in this calendar consists of a number, 1 to 13, and the name of a day, of which there were 20. The day glyphs are shown below.





















There was a lot of freedom in the drawing of Mayan glyphs; they could be drawn simply, or in detail. Please compare the above glyphs with those shown in these pages: Montgomery, Wikipedia.

In the Tzolk'in calendar, the numbers and days cycle together, like two interlocking gears. Suppose that today were 1 Imix. Tomorrow would be 2 Ik', and the day after tomorrow would be 3 Ak'bal. After 13 days, the cycle would reach 13 Ben. The next day, the numbers would start from 1 again: 1 Ix, 2 Men, etc. (See the diagram at right.) Twenty days after today, the date would be 7 Ajaw. Then, the cycle of day names would return to Imix: 8 Imix, 9 Ik', 10 Ak'bal etc.

Notice that this calendar has a cycle which repeats every 260 days (13 x 20 = 260). What is the use of such a calendar?

The Tzolk'in calendar was used for the same purpose as European astrology: divination. Each day in the 260-day cycle was associated with a god, and had its own character. The Maya used this calendar to determine which days were fortuitous for performing religious ceremonies, weddings, starting a trip, or a war, etc.

In some areas, the Tzolk'in calendar is still in use. Some Maya still consult 'calendar priests' who are considered experts in divination, for planning important events.

The Haab-Calendar

Haab means 'year' in the Yucatec language. In the Haab calendar, a year is always 365 days long. The ancient Maya knew that the year really lasts 365 days plus a quarter, but they didn't see any need to deal with that bothersome quarter day.

The Maya divided the year into 18 time periods (which are loosely called 'months') of 20 days, plus a short 5-day month, which was considered very unlucky. Each month had a name, and each day of the month had a number.




















Compare the above glyphs with these: Montgomery, Psychonauts.

The day numbers run from 1 to 19. The last day of a month is the 'sitting' of the next month. For example, in the month Xul, the dates are 1 Xul, 2 Xul etc. up until 19 Xul. The last day of Xul is 'chum Yaxk'in', which means, 'the sitting of Yaxk'in'. (Yaxk'in is the following month.)

The same applies to the short unlucky month Wayeb; the fifth day is 'chum Pop', 'the sitting of Pop'.

Together, the Calendar Cycle

In the Mayan system, to indicate the date of a specific day, the dates of the divination calendar and the year calendar are combined. For example 12 Lamat 15 Pop, or 4 Imix 18 Mol.

Imagine two gears which represent the two calendars: the Tzolk'in with 260 teeth, and the Haab with 365. The two gears turn together. How often does a specific day, for example 2 Men 19 Xul, return? If you multiply the number of days: 260 x 365 = 94900 days. But, the common factor of 260 and 365 is 5. Therefore, the cycle repeats every 18980 days (because 94900/5 = 18980). This is a cycle of 52 years (18980/365).

The beginning of a new 52-year period was an important event for the ancient Maya, as a change in century for us. They marked the occasion with new construction, for example, by enlarging their pyramids.

Long Count

A calendar which cycles every 52 years is not adequate for recording events which happened more than 52 years ago. (Similarly, with our Gregorian calendar, two digits are not enough for recording dates which happened more than a century ago.)

On their monuments, the Maya recorded dates using the 'Long Count'. ('Long Count' is a modern name.) The Long Count represents the number of days which have passed since the end of the previous Great Cycle, a period of 5125 years. The Great Cycle is discussed later.

To understand the Long Count, it's useful to learn the names of Mayan time divisions.

Mayan word  Signifo

winal20 days, (a Mayan month)
tun18 winal-s, 360 days, almost a year
k'atun20 tun-s, 7200 days, almost 20 years
bak'tun20 k'atun-s, 144000 days, approx. 400 years

A Mayan date is fully described by 5 numbers. For example, the famous king of Palenque, Hanab-Pakal, was born on


In total, 1357100 days after the end of the last Great Cycle.

Based on historical writings, Carbon-14 mesurements, and astronomical considerations, experts have succeeded in correlating Mayan dates with our calendar. They have calculated that the last day of the last Great Cycle corresponds to the 11th of August, 3114 BC (by the Gregorian calendar). Or the 12th. Or the 13th. Currently, opinions are almost evenly divided between the 11th and the 13th. The arguments for and against specific dates are too complicated to discuss in this short essay, but I believe that the 11th of August is the correct date. (Some Maya still user the divination calendar; their calendar supports the 11th of August.)

Hanab-Pakal was born 1357100 days after the 11th of August, 3114 BC. By rough calculations: 1357100 / 365.25 ~= 3716 years; 3716 years - 3114 (BC) = 602 AD. But, there was no year 0, so it's necessary to add 1: 602 + 1 = 603. Hanab-Pakal was born in the year 603.

When calculated precisely, the date was the 24th of March, 603 AD.

About the Great Cycle

The Great Cycle is a period of 13 baktuns, approximately 5125 years. The Maya based their Long Count dates on the last day of the Great Cycle, which they represented as . At present, we are in the thirteenth baktun (12.x.x.x.x). This baktun, and the current Great Cycle, will end on, which corresponds to the 21st of December, 2012 (or the 23rd of December, according to some sources).

Ancient Mayan myths tell of a series of destructions and recreations. Some superstitious people believe that the Maya predicted the end of humanity at the end of the current Great Cycle. But the Mayan calendarists defined cycles much longer than the Great Cycle. They believed that humanity will be destroyed at the end of some cycle, but they apparently did not suppose that that would happen in 2012.


Nothing described above is unique to the Maya. The number system, the divination calendar, the year calendar, and the 52-year cycle were common to all Mesoamerican people. No doubt many peoples borrowed ideas from the Maya, but the Maya also borrowed from other cultures. The Maya did not invent the calendar.

Also worth mentioning is that the Maya were not the first American people to use written language, and not even the second. The people who first invented writing may have been the Zapotecs, who lived and still live in the Mexican state Oaxaca. According to experts, the first Zapotec writings date from 600 to 400 BC.

The Zapotec writing system has not been deciphered, but it has been determined that they used the dot-line system to represent numbers. Based on this observation, experts have determined that the Zapotecs used a divination calendar of 260 days, and a year calendar of 365 days. Some even believe that the Zapotecs invented the calendar.

The Zapotec calendar had a 52-year cycle, but they did not use a Long Count; therefore, it is not possible to relate Zapotec dates with our calendar.

Early Long Count Dates

The earliest Long Count date yet discovered is, which corresponds to the fifth of December, 36 BC. This date was carved on a stela which was found at Chiapas de Corzo, in the state of Chiapas, Mexico. This region is outside the Mayan territory. Who made this stela, if not the Maya?

Early Long Count dates have been found with a written language, which is still undeciphered. It is different from Mayan and Zapotec writing, and there are very few surviving texts. The most famous are the Tuxtla Statuette, which has a date of (162-03-12 AD), and the Mojarra Stela, which has a text of about 400 glyphs, and two dates: (143-05-19 AD) and (156-07-11 AD).

This written language is known by more than one name: the Isthmian Script (because it was found in the Isthmus of Tehuantepec), the Mojarra Script (because of the Mojarra Stela, which has the longest text) and the Epi-Olmec Script ('after-Olmec', because the natives who used this script may have been direct descendants of the Olmec). (About the Epi-Olmec Script)

Currently in western Chiapas and the Isthmus of Tehuantepec, there are two related groups of indigenous people, the Mixe and the Zoque. In ancient times, the Olmec, who created the first Mesoamerican civilization, lived in the same area. Because of this, and linguistic considerations, many experts believe that the Olmec spoke an Mixe-Zoquean language, or, more specifically, an ancient form of the Zoquean language.

The Tuxtla Statuette and the Mojarra Stela were made long after the fall of the Olmec civilization, but the natives who made them may have been direct descendants of the Olmec, and ancestors of the modern Mixe and Zoque.

Mayan Dates

The earliest Long Count date recorded is (292-07-06 AD), which was found on a stela at Tikal, Guatemala. The last Long Count date was (909-01-20 AD), which was found at Toniná, Chiapas. Long Count dates are a defining characteristic of the Mayan Classic period, which some Mayanists define as 250 AD to 925 AD.

Short Count

After the fall of the Classic civilization, the Maya stopped using the Long Count. To record historical events, and to divine the future, they started using a system based on katuns. Mayanists call this system the 'Short Count', because it cycles every 13 katuns, which is 256 years. (The Long Count cycles every 13 baktuns, 5125 years.)

According to the Mayan way of thinking, not just the calendar, but history itself goes through cycles. If an important event happened during a specific katun, it would happen again after 256 years, during the katun of the same name. In the Mayan almanac Chilam Balam, history and divination are mixed with ambiguous dates, which is very confusing for modern historians.



Calendario Zapoteco / Zapotec Calendar
The Maya Calendar      Michael John Finley
La Majaa Mondo Klasika      Nombroj en la Majaa Lingvo
Dictionary of Maya Hieroglyphs, John Montgomery
Wikipedia: Maya Calendar      Jaguar-Sun
The Mayan Calendar, I. Van Laningham
Introduction to Maya Hierglyphs, Kettunen & Helmke



Michael D. Coe
1999 The Maya, 6th edition, Thames & Hudson, ISBN 0-500-28066-5
Michael D. Coe, Mark Van Stone
2005 Reading the Maya Glyphs, 2th edition, Thames & Hudson,
ISBN 0-500-28553-5
Sandy Huff
1984 The Mayan Calendar Made Easy, Area Maya / Mayan Area