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Mayan Long Count Calendar

Calculating the Mayan Long Count Calendar


Traditional Mesoamerican Numbering System

Traditional Mesoamerican Numbering System

K. Kris Hirst

The Mayan Long Count Calendar is a calendar system that was used by the ancient Maya civilization during the Classic period between AD 200 and 900. This entry in the Dictionary of Archaeology includes information on how the Long Count Calendar functions. See the main glossary entry for the Mayan Long Count for additional cultural information.

The Mayan Long Count Calendar and Base 20

The Mayan Long Count Calendar uses what mathematicians call base 20 or the vigesimal system. Western number systems, the ones English speakers are most familiar with, are in base ten or the decimal system. Scholars believe Mesoamericans used base 20 for the same reason others use base 10: because we humans have ten fingers and ten toes, and that's what we use to count with.

The innovation of the Maya Long Count Calendar required that the numbers have meaning when they are placed relative to one another ("positional meaning"), that there be a mathematical concept of zero, and that a starting date be created to anchor events in time.

The Mixe Zoque who invented the Mayan Long Count Calendar probably about 300 BC chose the year 3114 BC as its starting date, for reasons that are unknown to us. Scholars are divided as to the specific Gregorian calendar date meant by the starting date, represented by archaeologists as Estimated dates range between August 11 and September 8, 3114 BC.

Mayan Long Count Calendar Components

The Mayan Long Count vigesimal system is broken into five vigesimal columns.

  1. cycle or baktun = 20 k'atun = 144,000 days (~400 years)
  2. k'atun = 20 tun = 7200 days (~20 years)
  3. tun = 18 winal = 360 days (~1 year)
  4. uinal or winal = 20 k'in = 20 days (~month)
  5. k'in = 1 day

These are typically recorded by archaeologists translating the ancient Maya script, like this:

  • baktun.k'atun.tun.winal.k'in

Thus, In the same way that 2012 means two thousand, no hundreds, one ten and two ones,


means 12 baktun, 19 k'atun, 17 tun, 3 winal, and 6 k'in, or 15 March 2010. By the way, this combination of Arabic numerals is of course, a modern transcription of the Mayan number system. The traditional Mayan number system, also used in other Mesoamerican societies with some variations, used a series of dots and bars to represent numbers, with a shell icon representing zero, as illustrated in the image on this page.

This glossary entry is a part of the About.com Guide to the Maya Civilization and part of the Dictionary of Archaeology

Sources and Further Information

Clark JE, and A Colman. 2008. Time Reckoning and Memorials in Mesoamerica. Cambridge Archaeological Journal 18(1):93–99.

Edmonson MS. 1976. The Mayan Calendar Reform of Current Anthropology 17(4):713-717.

Estrada-Belli F. 2006. Lightning Sky, Rain, and the Maize God: The Ideology of Preclassic Maya Rulers at Cival, Peten, Guatemala. Ancient Mesoamerica 17:57-78.

Gasco, Janine. 2001. Calendrics. pp. 90-92 in The Archaeology of Ancient Mexico and Central America: An Encyclopedia Edited by Susan Toby Evans and David L. Webster. Garland Publishing Inc., New York

Marcus J. 2006. Mesoamerica: Scripts. p 16-27 in: Brown K, editor. Encyclopedia of Language & Linguistics. Second ed. London: Elsevier.

Marcus, Joyce and Kent V. Flannery. 2004. The coevolution of ritual and society: New 14C dates from ancient Mexico. Proceedings of the National Academy of Sciences 101(52):18257-18261. Free download.

Rice PM. 2009. On Classic Maya political economies. Journal of Anthropological Archaeology 28:70–84.

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