Maya Calendar
The Maya calendar was not as accurate as some have claimed. It is not even as accurate as the one introduced by Julius Caesar in 45 BC.

What were the Maya trying to accomplish?

Whenever we study another culture, we risk assuming that its members have the same priorities as we do. That risk may be greater when we study their calendar, because "everyone knows what a calendar is for". The following, from archaeoastronomer Anthony Aveni, might be good to keep in mind as you read about the Maya calendar:

Slippage between the 365-day year count and the actual year of 365.2422 days, measured by the annual course of the sun in the sky, did not seem to matter to the Maya. They did not on certain occasions add days to the year count, as we do with leap years to keep our holidays from sliding backward through the seasons. What if Christmas retreated into autumn or the Fourth of July backed up into the cold of winter? For reasons we will probably never know, the Maya seemed to place more emphasis on an unbroken chain of time, as they did with the tzolkin. They were different from us.1

The Structure of the Maya Calendar System

The Maya used two primary calendars: The sacred year of 260 days called the Tzolkin and the civil year of 365 days called the Haab. These calendars ran simultaneously. Because of the difference in length, the combination of the two dates uniquely identified each day in a 52 year cycle. The entire cycle was called the Calendar Round.

It is likely that the Maya calendar did not originate with the Maya, but rather originated in a previous culture and that other cultures such as the Aztec in turn also derived their calendar from similar sources.2

The Calendar Round was sufficient for most uses, as its duration exceeded the life expectancy of the typical Maya. However, to reference the passage of time for more than 52 years, the Maya used a third calendar called the Long Count.

The Tzolkin: The religious calendar

The Tzolkin (or "sacred" or "religious") calendar used a 260 day cycle. This calendar was in use throughout mesoamerica, and is not unique to the Maya. It is probably the oldest calendar in their system, and was perhaps the most important. The Maya likely inherited this calendar from preceding cultures.

The original purpose of devising such a calendar, with no obvious relation to any astronomical or geophysical cycle, is not known, but there are several suggested sources. A common idea is that the length of the calendar was based on multiplying 13 and 20, which were important numbers to the Maya. Twenty was the basis of the Maya counting system, and was taken from the number of human fingers and toes. Thirteen may have symbolized the number of levels in the Upperworld where the gods lived, or it may be a reference to the number of "joints" in the human body (ankles, knees, hips, shoulders, elbows, wrists, and neck).

Another idea is that the 260-day period came from the length of human pregnancy. This is close to the average number of days of gestation. It is also possible that the number 260 was noted as being a repeating pattern for some combination of the above reasons. Humans are good at finding patterns even where none exist. It may be possible that none of the above speculations are correct, and we simply don't know why 260 was chosen as a basis for the calendar.

While our calendar uses a single week of seven days, the Maya Tzolkin calendar used two different lengths of week:

  • a numbered week of 13 days, in which the days were numbered from 1 to 13
  • a named week of 20 days, in which the names of the days were:
0. Ahau 1. Imix 2. Ik 3. Akbal 4. Kan
5. Chicchan 6. Cimi 7. Manik 8. Lamat 9. Muluc
10. Oc 11. Chuen 12. Eb 13. Ben 14. Ix
15. Men 16. Cib 17. Caban 18. Etznab 19. Caunac

Since the numbered and the named week were running simultaneously, each of their names and numbers change daily. If a day was 3 Cimi, the following day is not 4 Cimi, but rather 4 Manik, and the day after that, 5 Lamat. The next time Cimi rolls around, 20 days later, it will be 10 Cimi instead of 3 Cimi. The next 3 Cimi will not occur until 260 days have passed. This 260-day cycle also had good-luck or bad-luck associations connected with each number/name combination, and was known as the "divinatory year."

The Haab: The Civil calendar

The Haab was the civil calendar. It consisted of 18 "months" of 20 days each, followed by 5 extra days, known as Uayeb. This gives a year length of 365 days.

The purpose of the Haab is more straightforward, and was designed to more or less track the solar year

The names of the months were:

1. Pop 2. Uo 3. Zip 4. Zotz 5. Tzec 6. Xul
7. Yaxkin 8. Mol 9. Chen 10. Yax 11. Zac 12. Ceh
13. Mac 14. Kankin 15. Muan 16. Pax 17. Kayab 18. Cumku

In contrast to the Tzolkin dates, the Haab month names changed every 20 days; so the day after 4 Pop would be 5 Pop, followed by 6 Pop, etc., up to 19 Pop, which is followed by 0 Uo. The days of the month were numbered from 0 to 19.

The Uayeb days were considered bad luck. They were known as "days without names" or "days without souls," and were observed as days of prayer and mourning. Fires were extinguished and the population refrained from eating hot food. Anyone born on those days was "doomed to a miserable life."

The Calendar Round

The length of the Tzolkin year was 260 days and the length of the Haab year was 365 days. The smallest number that can be divided evenly by 260 and 365 is 18,980 days, or 52 Haab years. This period was known as the Calendar Round. The 'New Years' days of the Tzolkin and Haab calendars fell on the same day once every 52 years. This became a date of importance to the Maya, and the number 52 also became very important to them. Scholars have found a large numerical table of multiples of 52 in the Dresden Codex. Every 52 years the Maya extinguished all of the fires in their households and threw away all their clay utensils. Then they “renewed” their social life by bringing a new fire (el fuego nuevo) from a central location into all the villages and cities.

The 'Calendar Round Date' consisted of the Tzolkin day number, followed by the Tzolkin day name (remember, these cycle with different period lengths), followed by the Haab date (day number followed by month name). An example might be 4 Ahau 8 Cumku which would be followed by 5 Imix 9 Cumku. The next time a day falls on 4 Ahau 8 Cumku would be 18,980 days or 52 Haab years later.

You can see today's date in the Maya calendar by going to this link.

The Long Count Calendar

The Long Count Calendar served the same purpose in the Maya culture as the numbered years serves in ours. When was the Magna Carta issued? 1215. When did Columbus sail west across the Atlantic? 1492. When was the Declaration of Independence signed? 1776. These numbers are understood in our culture to refer to a particular solar year. The Long Count calendar operated in a similar fashion as the modern Julian Day, in that it is merely a count of the days that have passed since a particular starting point. For the Julian Day that starting point is January 1, 4713 BC Greenwich noon (See the link above for an explanation of why this date was chosen). For the Maya long count calendar, that day was August 11, 3114 BC.

Structure of the Long Count

The Long Count calendar kept time in units of 20, so 20 days made a uinal, 18 uinals, or 360 days, made a tun, 20 tuns made a katun, and 20 katuns, or 144,000 days, made up a baktun. After 13 baktuns, the numbers reset and the count moved to a higher order.3 The Maya encoded these values in glyphs, but we represent the glyphs with numbers separated by periods. So, for example, the Maya date of represents 8 baktuns, 3 katuns, 2 tuns, 10 uinals and 15 days since creation. Today, the most widely accepted correlations of the end of the thirteenth baktun, or Maya date, with the Western calendar are either December 21 or December 23, 2012.4

At the New York Times, there is a handy little long count calendar calculator, that you can use to see the long count for any date.


With one exception, the calendars did not 'synchronize' with each other on an annual basis. Because the named Tzolkin week is 20 days long, and the smallest Long Count digit is 20 days, the smallest Long Count digit also represents the Tzolkin named day. For example, the last digit of today’s Long Count is 0, today is Ahau; if it is 6, it is Cimi. However the Long Count does not synchronize to the Tzolkin or Haab in any other way.

As noted above, the length of the Tzolkin and Haab formed the length of the 'Calendar Round' cycle when multiplied together. So the Calendar Round formed a repeating pattern on a 52 Haab year cycle.

So the Maya had at least three calendars running simultaneously, none of which were in sync. They also had other calendars for other purposes, such as tracking the cycles of Venus.

Use of the Long Count

The Long Count was useful for uniquely identifying particular dates in history. Something that is going to be carved in stone will generally last more than 52 years, so the Calendar Round date would quickly become confusing. Using the Long Count date instead of the Calendar Round date insures that the date recorded on a monument is well understood hundreds of years later.

The Long Count was given as a 'distance' date, indicating the number of days since the date of creation in their mythology. As a result, it is inevitable that it would occasionally reach round figures.

Having removed some of the mystery surrounding the Maya Long Count calendar, we can now see that a round number in the long count is not mysterious at all, but rather an inevitable consequence of counting the days since a given starting point.


There are a lot of rumors currently circulating about the Maya calendar. Most of them have nothing to do with the facts.

The Maya did not invent the Mesoamerican calendar

As noted above, the Maya likely inherited the Tzolkin and perhaps the Haab from preceding cultures. These calendars were used throughout the region, and it is likely that all of the contemporaries of the Maya inherited their calendars from common or similar sources. That source is frequently identified with the Olmecs, although there is considerable debate about them as the originator of the calenders. Other potential sources are sometimes cited as the Zapotec and Mixtec cultures.

The Maya were not the Aztec


Most of the time that proponents of the 2012 hoax reference pictures of "the maya calendar" they show a picture of the Aztec sun stone instead. Even the cartoon to the right commits this error.

Check out this quote from Johan Normark:

Yes, the calendar stone looks great but it has nothing to do with the long count. The Aztec did not derive their calendar from the Maya but from a more “general Mesoamerican tradition”.The Maya and Aztec calendars can therefore be traced back to earlier Mesoamerican calendars (such as Zapotec). Check this quote from Wikipedia (which is correct):

“The Central Mexican calendar system is best known in the form that was used by the Aztecs, but similar calendars were used by the Mixtecs, Zapotecs, Tlapanecs, Otomi, Matlatzinca, Totonac, Huastecs, P’urhépecha and at Teotihuacan. These calendars differed from the Maya version mainly in that they didn’t use the long count to fix dates into a larger chronological frame than the 52-year cycle.”5

So the Long Count calendar appears to be a feature of the Maya calendar that does not appear in many other Mesoamerican calendars. However, the rest of the calendar system does not appear to be uniquely Maya.

Furthermore, Normark points out that much of what we know about the ancient Maya comes from the Popol Vuh, a book compiling details of creation accounts known to the K’iche’ Maya of the Colonial-era highlands. In other words, the Popol Vuh was not written until the mid-1500's, several hundred years after the classic Maya civilization had vanished and the area had been under Aztec influence, potentially influencing the culture.6


The Maya calendar was particularly accurate for its time and place. We have already indicated above that the Maya calendar was not as accurate as the Roman Julian calendar. When compared to the solar year, the Julian calendar had an error rate of 1 day every 128 years. The modern Gregorian calendar is substantially more accurate, with an error rate of 1 day every 3,300 years.7 In contrast, the Maya calendar, which did not use any system of leap days, had an error rate of 1 day every 4 years when compared to the solar year.

Despite the fact that the Maya Haab is less accurate when compared to the solar year than the Julian calendar is, and much less accurate than the modern Gregorian calendar , some people are using the supposed accuracy of the Maya calendar to claim that they obviously had everything right, where our modern calendar has it wrong. We have seen outrageous claims made about the accuracy of the Maya calendar: that it kept in perfect sync without "leap" days, that it is more accurate than the modern calendar, that it kept perfect time over thousands of years.

This is bunk. Claims of accuracy and precision are specious because they are comparing apples and oranges. The Gregorian calendar is primarily a solar calendar. The Haab was primarily a solar calendar. The Tzolkin, 'Calendar Round' and 'Long Count' calendars are not solar calendars. We will compare the modern Gregorian calendar with the Haab and see just how accurate it was.

No solar calendar ever devised can do away with some form of leap days (or "intercalary days"), for these simple reasons:

  1. There is not an integer number of days in a year (365.2524 days per year)8
  2. There is not an integer number lunar cycles in a year (12.3683 lunar cycles per year)9
  3. There is not an integer number of days in a lunar cycle (29.53059 days per lunar cycle).10

It would be nice if things were different, and there were exactly an even number of days per lunar phase, and an even number of lunar phases per year, but that's just not how it is.

No astronomical year has an integer number of days or lunar months, so any calendar that follows an astronomical year must have a system of intercalation such as leap years.


The number of mean solar days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more.11

That last number is the reason why no solar calendar can do without leap days, unless the calendar is going to ignore the seasons. So, because our year is about (but not quite) 1/4 of a day longer than 365 days, the Gregorian calendar has a leap year, a year with an extra day, every four years (the complete rules are a bit more complex than that). Because of other influences, you may hear from time to time that a ‘leap second’ is being added or subtracted from the atomic clocks. This constant fiddling with the calendar is necessary to keep it accurate and does not indicate that it is inaccurate.

Furthermore, as we show above, the Maya civil calendar, the Haab used an intercalary month called the Uyaeb: The "days without names". Whoops? What was that? An intercalary month? In addition, there is evidence that the Maya knew that the haab was not in time with the solar year, but that there is no evidence that they did anything about it.12

So, we contend that the Maya solar calendar was less accurate than the modern Gregorian calendar, from any reasonable definition of ‘accurate’. It was also less accurate than the Roman Julian calendar.

Cycles within cycles

How did the Maya resolve this disconnect between the Haab or 'civil calendar' and the solar year? Apparently it was the duty of the Jaguar Priests to tell the Maya when to plant crops, etc.

There is evidence that the Maya knew that the Haab did not exactly correspond with the solar year, but they did not make any adjustments to it. Some authors contend that the Mayas estimated that a 365-day year precessed through all the seasons twice in or 1,101,600 days. However, what the Maya knew or calculated is frequently built on speculation and incomplete data.

It seems likely that they were not unduly troubled by this, even though it meant the Haab drifted away from the solar year by one day every four years. Perhaps they saw it as simply another cycle? Therefore it appears that the Maya were comfortable with one Haab month falling in midsummer at one point, but falling in midwinter hundreds of years later.

The fact that the Maya ignored leap years does not mean that the calendar correlation is wrong

Early in 2012, the following message appeared on Facebook:

There have been about 514 Leap Years since Caesar created it in 45BC. Without the extra day every 4 years, today would be July 28, 2013.
Also, the Mayan calendar did not account for leap year…. so technically the world should have ended 7 months ago.

This message has been repeated thousands of times on Twitter, YouTube and numerous discussion forums. However, there are a number of problems with it.

Firstly, as we have said on this page, the Maya did not use leap years for the reason that they were not attempting to keep exactly in step with the solar year. This has been well known ever since their calendars were first researched more than a century ago.

Secondly, the December 2012 date depends on the Long Count which is a count of days and is a different calendar from the approximately seasonal Haab.

Thirdly, it doesn't really matter whether any calendar is 'right' or 'wrong' or has been modified. What's important is that we know how it works and know the rules for arriving at a particular date.

At this point, it should be explained how the date of 21st December 2012 was deduced. The most widely accepted correlation between the Long Count and the Gregorian calendar is the Goodman-Martinez-Thompson (GMT) correlation which places the start of the Long Count as 11th August 3114 BCE in the Gregorian calendar.13

So we know when the Long Count began and how it counts forward. We know how the Gregorian calendar works and how many leap years it has. Thus we can count forward 13 baktuns of 144,000 days each, totalling 1,872,000 days, starting from 11th August 3114 BCE. Taking into account all leap years, we arrive at a date of 21st December 2012.


In conclusion; we have shown that the Maya calendar was not as accurate as the modern Gregorian calendar, and that it was not even as accurate as the older Julian calendar. The fact that the Long Count calendar reaches a round number is an inevitable consequence of counting the number of days since a given starting point.

1. Aveni, Anthony. 2009. The End of Time: The Maya Mystery of 2012, University Press of Colorado, Boulder. Available for free viewing online at
2. Malmström, Vincent H. undated. The Astronomical Insignificance of Maya Date Dartmouth College.
3. Mills, David L., PhD. 1995. The Classic Maya Calendar and Day Numbering System (accessed 2009-03-25)
4. Normark, Johan. PhD. 2009-07-03. Personal communication.
5. Normark, Johan, PhD. 2009. 2012: How to spot a prophet’s Maya hoax – The Aztec calendar stone Archaeological Haecceities (accessed 2009-07-22)
6. Robbins, Stuart. 2009. Planet X & 2012: Primer on the Mayan Calendar (accessed 2009-03-25)
7. Sitler, Robert K. 2006. The 2012 Phenomenon: New Age Appropriation of an Ancient Mayan Calendar. (accessed 2009-07-23)
8. Wikipedia. 2009. Gregorian Calendar (accessed 2009-05-30)
9. Wikipedia. 2009. Lunar Phase (accessed 2009-06-01)
10. Wikipedia. 2009. Tropical Year (accessed 2009-03-25)
11. Wikipedia. 2009. Year: Calendar Year (accessed 20090-04-21)


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