Mayan Calendar Converter | Long Count to Gregorian

Mayan calendar converter

A Mayan-Gregorian calendar converter translates dates between the Maya Long Count calendar and the modern Gregorian calendar. The Long Count is a day-counting system the ancient Maya used to record dates on stone monuments, buildings, and painted books. Converting between the two systems lets historians, archaeologists, and students match Maya dates to familiar Gregorian ones.

What is the Mayan Long Count calendar?

The Long Count is a vigesimal, or base-20, counting system. It counts the days that have passed since a fixed starting point in Maya belief: August 11, 3114 BCE on the proleptic Gregorian calendar (the Gregorian calendar extended backward before it actually existed). Unlike a calendar with fixed months and leap years, the Long Count is just a running day count, similar to an odometer.

A Long Count date has five positions, written largest to smallest and separated by dots:

• Baktun – 144,000 days, about 394 years
• Katun – 7,200 days, about 20 years
• Tun – 360 days, close to one year
• Uinal – 20 days
• Kin – 1 day

Each position rolls over into the next once it reaches its limit. Baktun, katun, and tun each hold values from 0 to 19, since the system is base-20. The uinal is the exception: it holds values from 0 to 17, because 18 uinals (18 × 20 = 360 days) make one tun instead of 20. This adjustment keeps the tun close to the length of a solar year.

The word "kin" also means "sun" in several Mayan languages, since it marks a single day.

A date is written as baktun.katun.tun.uinal.kin. For example, 13.0.0.0.0 means 13 baktuns, 0 katuns, 0 tuns, 0 uinals, and 0 kins have passed since the starting point. That date fell on December 21, 2012, the day the 13th baktun finished and the 14th began.

How to convert a Mayan Long Count date to Gregorian

Converting a Long Count date to a Gregorian date takes three steps.

Step 1: Add up the total days. Multiply each unit by its day value and add the results.

Step 2: Add the correlation constant. The Goodman-Martinez-Thompson (GMT) correlation constant, 584,283, is the Julian Day Number (a continuous day count used by astronomers) that matches the Maya starting date, 0.0.0.0.0. Adding it to the total days gives the Julian Day Number for the target date.

Step 3: Convert the Julian Day Number to a Gregorian date. This uses a standard astronomical formula that accounts for leap years and month lengths.

Example

Convert the Long Count date 9.12.11.5.18:

Julian Day Number: 1,386,478 + 584,283 = 1,970,761

Converting Julian Day Number 1,970,761 to a Gregorian date gives August 29, 683 CE.

How to convert a Gregorian date to a Mayan Long Count date

This reverses the process.

Step 1: Convert the Gregorian date to a Julian Day Number using the standard astronomical formula.

Step 2: Subtract the correlation constant: Julian Day Number − 584,283 = days since the Maya starting point.

Step 3: Divide the result by each unit's day value, in order from largest to smallest, keeping the remainder each time.

Example

Convert January 1, 2000 to a Long Count date:

• Julian Day Number for January 1, 2000: 2,451,545
• Days since 0.0.0.0.0: 2,451,545 − 584,283 = 1,867,262
• Baktun: 1,867,262 ÷ 144,000 = 12, remainder 139,262
• Katun: 139,262 ÷ 7,200 = 19, remainder 2,462
• Tun: 2,462 ÷ 360 = 6, remainder 302
• Uinal: 302 ÷ 20 = 15, remainder 2
• Kin: 2

Result: 12.19.6.15.2

The GMT correlation constant

The GMT correlation constant ties the Maya calendar to the Julian Day Number system, and from there to the Gregorian calendar. It states that the Maya date 0.0.0.0.0 equals Julian Day Number 584,283, which falls on August 11, 3114 BCE in the proleptic Gregorian calendar.

Most Maya scholars accept the GMT value. The evidence comes from several directions:

• Colonial records. Spanish colonial writers, including Bishop Diego de Landa in the 16th century, recorded Maya dates alongside European ones.
• Astronomy. Maya texts describe events like Venus risings and eclipses. Modern astronomers can calculate when those events actually happened and check the match.
• Radiocarbon dating. Wood beams from dated Maya buildings have been tested with radiocarbon dating, and the results line up with GMT-based dates.
• Internal consistency. GMT produces a sensible order of events, such as royal successions and building dedications, across different Maya cities.

A few alternative correlations exist, mostly differing by multiples of 260 days, the length of the Tzolk'in sacred calendar (explained below). The Spinden correlation, for example, is about 260 years earlier than GMT. Most current archaeological evidence favors GMT over these alternatives.

Other Maya calendars

The Long Count was not the only calendar the Maya used. It usually appeared alongside two cyclical calendars.

Tzolk'in. A 260-day sacred calendar made by combining 13 numbers with 20 named days. It was used for religious ceremonies and divination and did not track solar years.

Haab. A 365-day civil calendar made of 18 months of 20 days each (360 days), plus a short 5-day period called Wayeb at the end of the year. The Haab had no leap-year correction, so it slowly drifted out of step with the actual solar year.

Combined, a Tzolk'in date and a Haab date make up a Calendar Round, which repeats every 52 Haab years, or 18,980 days. A Calendar Round date alone cannot fix an event to one specific year, since the same combination returns every 52 years. The Long Count avoids this problem because it never repeats.

The Long Count and December 21, 2012

The Long Count date 13.0.0.0.0 fell on December 21, 2012. This marked the end of the 13th baktun since creation, a length of time called a Great Cycle, about 5,125 years. Some popular media described this as a predicted apocalypse. Maya texts and modern Maya communities describe it differently: as the close of one long cycle and the start of the next, similar to a Gregorian century ending. The Long Count kept counting normally afterward, into the 14th baktun.

Frequently asked questions

What is the Mayan Long Count calendar? It is a day-counting system the ancient Maya used to record absolute dates. It counts days since a fixed starting point, August 11, 3114 BCE, using five place values: baktun, katun, tun, uinal, and kin.

What is the GMT correlation constant? It is the number, 584,283, that links the Maya calendar to the Julian Day Number system used by astronomers. It states that Julian Day Number 584,283 corresponds to the Maya date 0.0.0.0.0.

How do you convert a Mayan Long Count date to a Gregorian date? Multiply each unit (baktun, katun, tun, uinal, kin) by its day value, add the results, then add 584,283 to get a Julian Day Number. Convert that Julian Day Number to a Gregorian date using a standard astronomical formula.

Why does the Mayan calendar use base 20? The Maya used a vigesimal, or base-20, number system, likely based on counting fingers and toes. The Long Count adjusts this slightly: 18 uinals make one tun instead of 20, which keeps the tun close to the length of a solar year.

What happened on December 21, 2012 in the Maya calendar? The Long Count reached 13.0.0.0.0, completing the 13th baktun since creation. It marked the end of one long cycle and the start of another, not a predicted end of the world.

Do Maya communities still use the Long Count today? Most contemporary Maya calendar keepers, known as Ajq'ijab', focus on the 260-day Tzolk'in for ceremonies and divination. The Long Count is less common in daily use but remains an important part of Maya history and heritage.