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Maya Calendar — Tzolkʼin, Haabʼ and Long Count

Converts any date to the three Maya counts using the Goodman–Martínez–Thompson correlation, and shows the arithmetic that makes them turn: 260 days from thirteen numbers and twenty names, a 365-day year with no leap day, and a base-20 tally with one base-18 digit.

A date converter for the three Maya counts — the 260-day Tzolkʼin, the 365-day Haabʼ and the Long Count — with the correlation constant stated and the arithmetic shown. It is calendrics, not divination, and the page opens by saying so.

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For fun

The calendar arithmetic here is exact and checkable. What a day sign is supposed to say about a person is not part of it: those readings are modern, and this page does not carry them.

A converter, not a fortune. The three Maya counts are exact calendars; the personality readings attached to the day signs elsewhere are modern inventions, and are not here.

Tzolkʼin — the 260-day count

6 Ebʼ

6 Ebʼ. A number 1–13 and one of twenty names, both advancing every day, so the pair repeats after lcm(13, 20) = 260 days.

Haabʼ — the 365-day year

5 Keh

5 Keh. Eighteen months of twenty days numbered 0–19, plus the five-day Wayebʼ. There is no leap day, so the Haabʼ slips a day against the seasons every four years.

Long Count

13.0.14.1.12

13.0.14.1.12 — 1,877,072 days from the zero point. Written baktun.katun.tun.uinal.kin, base 20 except the uinal, which is 18, so that a tun is 360 days.

Calendar round

Day 17,033 of 18,980. The Tzolkʼin and Haabʼ realign every lcm(260, 365) = 18,980 days, about 52 years — the longest span the two counts alone can name without repeating.

This Tzolkʼin day comes round again — Every 260 days: 2027-07-28, 2028-04-13, 2028-12-29

The one number that could be wrong

Everything above depends on the correlation constant — the Julian Day Number of Long Count 0.0.0.0.0. This uses the Goodman–Martínez–Thompson value, 584283, which radiocarbon dates and the surviving Colonial-period day counts support and nearly all modern work uses. Its famous consequence: 13.0.0.0.0 falls on 21 December 2012, as 4 Ajaw 3 Kʼankʼin. The tests assert exactly that date, so if the constant were ever changed here, they would fail.

GMT = 584283 · calendar round = 18,980 days

The twenty day names

  1. 1Imix
  2. 2Ikʼ
  3. 3Akʼbʼal
  4. 4Kʼan
  5. 5Chikchan
  6. 6Kimi
  7. 7Manikʼ
  8. 8Lamat
  9. 9Muluk
  10. 10Ok
  11. 11Chuwen
  12. 12Ebʼ
  13. 13Bʼen
  14. 14Ix
  15. 15Men
  16. 16Kibʼ
  17. 17Kabʼan
  18. 18Etzʼnabʼ
  19. 19Kawak
  20. 20Ajaw

The nineteen Haabʼ months

  1. 1Pop
  2. 2Woʼ
  3. 3Sip
  4. 4Sotzʼ
  5. 5Sek
  6. 6Xul
  7. 7Yaxkʼin
  8. 8Mol
  9. 9Chʼen
  10. 10Yax
  11. 11Sakʼ
  12. 12Keh
  13. 13Mak
  14. 14Kʼankʼin
  15. 15Muwan
  16. 16Pax
  17. 17Kʼayabʼ
  18. 18Kumkʼu
  19. 19Wayebʼ

Sources

  • Correlation: Goodman–Martínez–Thompson, JDN 584283 for Long Count 0.0.0.0.0.
  • Day and month names in the standard Yucatec orthography, which is what the modern literature uses. The Classic-period Chʼoltiʼ names were different.
  • Gregorian dates are converted through this site’s own Julian Day Number routine, proleptic before 1582.

How to use it

  1. Enter any date

    Gregorian, proleptic before 1582. The zero point of the Long Count is 11 August 3114 BCE on that reckoning, and the tool will convert dates before it as negative day counts.

  2. Check it against 21 December 2012

    Everything depends on one number, the correlation constant. Enter that date and you should get 13.0.0.0.0, 4 Ajaw 3 Kʼankʼin — the reading that made the date famous. The tests assert exactly this, so the constant cannot drift unnoticed.

Common questions

What does my day sign mean?

This page does not say, because the sources do not. The Tzolkʼin named days and scheduled ritual; the personality readings attached to each sign in modern books are 20th-century constructions with no line back to the Classic-period record. The names are given in Yucatec Maya, which is worth more to a reader than an invented paragraph.

Why does the Haabʼ drift?

Because it has 365 days and no leap day. The Maya knew the year is about a quarter of a day longer and did not correct the count, so the Haabʼ slips a day against the seasons every four years. The Long Count, being a plain tally of days, does not drift at all.

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