Understanding the Maya Calendar System
The Maya did not use a single calendar — they tracked time with three interlocking systems at once. The Long Count is a linear day-count (like a Julian Day Number) that never repeats. The Tzolk'in is a 260-day cycle combining a number (1-13) with one of 20 day names, used for ritual and divination. The Haab' is a 365-day "vague year" of eighteen 20-day months plus a short 5-day month, used for civil and agricultural purposes. This converter turns any Gregorian date into all three at once.
Step 1: Gregorian date to Julian Day Number
The calculator first converts your Gregorian year, month, and day into a Julian Day Number (JDN) — a continuous day count used by astronomers, with no months or years, running proleptically backward before the Gregorian calendar's 1582 adoption. This uses the standard Fliegel-Van Flandern algorithm.
Step 2: Subtract the correlation constant
Subtracting the GMT correlation constant, 584283, from the JDN gives the Maya Long Count day total. This constant is itself a Julian Day Number: the JDN of the Maya creation date 0.0.0.0.0, 4 Ajaw 8 Kumk'u, which falls on 11 August 3114 BCE on the proleptic Gregorian calendar. Long Count day total = JDN − 584283.
Step 3: Decompose the Long Count
The Long Count day total is broken into five place values, each a fixed multiple of days: baktun (144,000 days), katun (7,200 days), tun (360 days), winal (20 days), and kin (1 day) — written baktun.katun.tun.winal.kin, the same way a decimal number is broken into place values, except the tun-to-winal step uses base 18 instead of base 20.
Step 4: Tzolk'in and Haab' from the same day total
The Tzolk'in number is ((Long Count total + 3) mod 13) + 1, and the Tzolk'in day name is selected by (Long Count total + 19) mod 20 from the 20-name list starting with Imix. The Haab' position is (Long Count total + 348) mod 365, which maps to a month and day within that 365-day cycle.
Worked example: December 21, 2012
This date is famous because it completed the 13th baktun. Its Julian Day Number is 2,456,283, giving a Long Count total of 1,872,000 days — exactly 13 × 144,000, so the Long Count reads 13.0.0.0.0. Working through the same day total gives Tzolk'in 4 Ajaw and Haab' 3 K'ank'in, matching the historically recorded inscription for that day. The 13th baktun completing was a milestone, not an ending — the Long Count simply rolled to 13.0.0.0.1 the next day, the same way an odometer keeps counting past all-nines.
The correlation constant is a scholarly consensus, not a certainty
584283 is supported by cross-referencing colonial-era Maya and Spanish document pairs, recorded astronomical events (eclipses, Venus cycles), and continuous day-keeping among modern highland Maya communities. A small number of older sources use 584285 instead, a 2-day difference traced to a Julian/Gregorian mix-up in early correlation studies; this calculator supports both so you can match whichever source you are checking against.