Mayan Calendar Converter

Convert dates between Gregorian and Mayan calendar systems including Tzolkin, Haab, and Long Count.

This calculator converts dates between the modern Gregorian calendar and the ancient Mayan calendar system, which includes the Tzolkin (260-day sacred calendar), Haab (365-day solar calendar), and Long Count (linear time measurement).

Example Conversions

Click on any example to load it into the calculator.

December 21, 2012

gregorian_to_mayan

The famous end of the 13th Baktun date that was predicted as the end of the world.

Input Type: undefined

Gregorian Date: 2012-12-21

13.0.0.0.0

mayan_to_gregorian

The completion of the 13th Baktun, marking the end of a major cycle in Mayan cosmology.

Input Type: undefined

Baktun: 13

Katun: 0

Tun: 0

Uinal: 0

Kin: 0

January 1, 2000

gregorian_to_mayan

The beginning of the new millennium in the Gregorian calendar.

Input Type: undefined

Gregorian Date: 2000-01-01

9.17.0.0.0

mayan_to_gregorian

A significant date in Mayan history, marking the completion of the 9th Baktun.

Input Type: undefined

Baktun: 9

Katun: 17

Tun: 0

Uinal: 0

Kin: 0

Other Titles
Understanding Mayan Calendar Converter: A Comprehensive Guide
Master the conversion between modern Gregorian dates and ancient Mayan calendar systems. Learn about Tzolkin, Haab, Long Count, and the mathematical principles behind Mayan timekeeping.

What is the Mayan Calendar System?

  • Three Interlocking Calendars
  • Sacred and Solar Cycles
  • Linear Time Measurement
The Mayan calendar system is one of the most sophisticated ancient timekeeping systems ever developed. Unlike the single calendar we use today, the Maya used three interlocking calendars that worked together to track different aspects of time: the Tzolkin (sacred calendar), the Haab (solar calendar), and the Long Count (linear time measurement). This complex system allowed the Maya to track both cyclical and linear time with remarkable precision.
The Tzolkin: The Sacred 260-Day Calendar
The Tzolkin, also known as the Sacred Round, is a 260-day calendar that combines 13 numbers with 20 day names. This creates a cycle where each day has both a number (1-13) and a name (Imix, Ik, Akbal, etc.). The Tzolkin was used for religious ceremonies, divination, and determining auspicious dates. The 260-day period corresponds to the human gestation period and the agricultural cycle, making it deeply significant in Mayan culture.
The Haab: The 365-Day Solar Calendar
The Haab is the Mayan solar calendar, consisting of 18 months of 20 days each, plus a 5-day period called Wayeb. This creates a 365-day year that tracks the solar cycle. Each month has a specific name (Pop, Uo, Zip, etc.) and the days within each month are numbered 0-19. The Haab was used for agricultural planning and civil administration, similar to how we use the Gregorian calendar today.
The Long Count: Linear Time Measurement
The Long Count is a linear system for measuring time that can count forward indefinitely. It uses five units: Kin (1 day), Uinal (20 days), Tun (360 days), Katun (7,200 days), and Baktun (144,000 days). The Long Count begins from a mythical creation date (August 11, 3114 BCE in the Gregorian calendar) and can express dates millions of years into the future or past.

Key Concepts Explained:

  • Tzolkin Cycle: 13 numbers × 20 day names = 260 unique combinations
  • Haab Structure: 18 months × 20 days + 5 Wayeb days = 365 days
  • Long Count Units: Kin (1), Uinal (20), Tun (360), Katun (7,200), Baktun (144,000)
  • Calendar Round: 52-year cycle when Tzolkin and Haab align

Step-by-Step Guide to Using the Mayan Calendar Converter

  • Input Selection and Validation
  • Mathematical Conversion Process
  • Result Interpretation and Verification
Using the Mayan Calendar Converter requires understanding both the input format and the mathematical conversion process. The calculator can convert in both directions: from Gregorian dates to Mayan calendar dates, and from Mayan Long Count dates to Gregorian dates. Each conversion involves complex mathematical calculations using Julian Day Numbers as an intermediate step.
Gregorian to Mayan Conversion Process
To convert a Gregorian date to Mayan calendar format, the calculator first converts the Gregorian date to a Julian Day Number (JDN). The JDN is then used to calculate the Long Count date by subtracting the Mayan epoch (JDN 584,283). The Tzolkin date is calculated using modulo arithmetic on the JDN, while the Haab date requires accounting for the 365-day solar cycle and the 5-day Wayeb period.
Mayan to Gregorian Conversion Process
Converting from Mayan Long Count to Gregorian date involves reversing the process. The Long Count values are converted to days since the Mayan epoch, then added to the epoch JDN to get the target JDN. This JDN is then converted to the corresponding Gregorian date. The Tzolkin and Haab dates are calculated using the same mathematical principles as in the forward conversion.
Validation and Error Handling
The calculator includes comprehensive validation to ensure accurate conversions. It checks that Long Count values are within valid ranges (Baktun: 0-19, Katun: 0-19, Tun: 0-19, Uinal: 0-17, Kin: 0-19), validates Gregorian dates, and handles edge cases such as leap years and calendar reforms. The calculator also provides error messages for invalid inputs and ensures mathematical precision.

Usage Guidelines:

  • Input Validation: Ensure all Long Count values are within valid ranges
  • Date Selection: Use the date picker for Gregorian dates or manual entry for Long Count
  • Result Verification: Cross-check results using multiple conversion tools
  • Historical Context: Consider the historical significance of converted dates

Real-World Applications of Mayan Calendar Conversion

  • Archaeological Research
  • Cultural Preservation
  • Astronomical Studies
  • Historical Analysis
Mayan calendar conversion has numerous practical applications in modern research and cultural preservation. Archaeologists use these conversions to date ancient Mayan artifacts and inscriptions, while historians analyze Mayan historical records. The precise astronomical knowledge embedded in the Mayan calendar system continues to inform modern astronomical research and cultural studies.
Archaeological Dating and Research
Archaeologists frequently encounter Mayan dates inscribed on monuments, stelae, and artifacts. Converting these dates to the Gregorian calendar allows researchers to correlate Mayan historical events with other world civilizations and establish accurate chronologies. The Long Count's precision enables dating of events to specific days, providing unprecedented accuracy for ancient history.
Cultural Heritage and Education
Mayan calendar conversion tools help preserve and promote understanding of Mayan culture and heritage. Educational institutions use these conversions to teach about ancient civilizations, while cultural organizations use them for traditional ceremonies and celebrations. The mathematical sophistication of the Mayan calendar system demonstrates the advanced knowledge of ancient Mesoamerican civilizations.
Astronomical and Scientific Applications
The Mayan calendar's astronomical accuracy makes it valuable for studying ancient astronomical knowledge and celestial events. Researchers use Mayan dates to correlate with astronomical phenomena such as eclipses, planetary alignments, and seasonal changes. This information helps reconstruct ancient astronomical observations and understand how the Maya tracked celestial cycles.

Practical Applications:

  • Archaeological Dating: Converting inscribed dates on Mayan monuments
  • Historical Research: Correlating Mayan events with world history
  • Cultural Education: Teaching about ancient Mesoamerican civilizations
  • Astronomical Studies: Analyzing ancient celestial observations

Common Misconceptions and Correct Methods

  • End of the World Predictions
  • Calendar Accuracy Myths
  • Mathematical Precision
  • Cultural Context
The Mayan calendar system has been subject to numerous misconceptions, particularly regarding the 2012 'end of the world' prediction. Understanding the mathematical and cultural context of the Mayan calendar helps dispel these myths and appreciate the true sophistication of this ancient timekeeping system. The calendar was designed to track time indefinitely, not predict apocalyptic events.
The 2012 Phenomenon and Calendar Cycles
The widely misunderstood 'end of the world' prediction for December 21, 2012, was based on the completion of the 13th Baktun in the Long Count. However, this was simply the end of one cycle and the beginning of another, similar to how our calendar rolls over from 1999 to 2000. The Maya never predicted the end of the world; they simply marked the completion of a major time cycle.
Mathematical Precision and Accuracy
The Mayan calendar system is remarkably accurate and mathematically sophisticated. The Long Count can express dates millions of years into the future or past, while the Tzolkin and Haab cycles provide precise tracking of both sacred and solar time. The system's mathematical foundation is based on careful astronomical observations and complex calculations that rival modern timekeeping methods.
Cultural and Religious Significance
The Mayan calendar was not merely a tool for tracking time but a fundamental aspect of Mayan religion, culture, and worldview. Each day in the Tzolkin had specific spiritual significance, and the calendar was used for divination, religious ceremonies, and determining auspicious times for important activities. Understanding this cultural context is essential for appreciating the calendar's true purpose.

Myths Debunked:

  • End of World Myth: 2012 marked cycle completion, not apocalypse
  • Primitive Technology: Mayan calendar was mathematically sophisticated
  • Lost Knowledge: Calendar principles are well understood by scholars
  • Cultural Superiority: Each calendar system serves its cultural needs

Mathematical Derivation and Examples

  • Julian Day Number Calculations
  • Modulo Arithmetic
  • Calendar Round Mathematics
  • Precision and Accuracy
The mathematical foundation of Mayan calendar conversion relies on Julian Day Numbers (JDN) as an intermediate step. JDNs provide a continuous count of days since January 1, 4713 BCE, making them ideal for calendar conversions. The conversion process involves complex modulo arithmetic and careful handling of calendar cycles to ensure accuracy across thousands of years.
Julian Day Number Foundation
Julian Day Numbers provide a continuous, linear count of days that serves as the mathematical foundation for calendar conversions. The Mayan epoch (August 11, 3114 BCE) corresponds to JDN 584,283. To convert a Gregorian date to Mayan, we first convert to JDN, then subtract the Mayan epoch to get days since the Mayan creation date. This number is then converted to Long Count units using division and modulo operations.
Tzolkin and Haab Calculations
The Tzolkin date is calculated using modulo arithmetic: (JDN - Mayan epoch) mod 260. This gives the day number within the 260-day cycle. The Haab date calculation is more complex, requiring conversion to the 365-day solar year and accounting for the 5-day Wayeb period. The Calendar Round, which combines Tzolkin and Haab, repeats every 18,980 days (52 years).
Precision and Error Handling
Mayan calendar conversion requires careful attention to mathematical precision, especially when dealing with dates spanning thousands of years. The calculator handles leap years, calendar reforms, and edge cases to ensure accurate conversions. Error checking validates input ranges and provides meaningful error messages for invalid dates or Long Count values.

Mathematical Examples:

  • JDN Calculation: Converting Gregorian dates to Julian Day Numbers
  • Long Count Conversion: Days since epoch to Baktun/Katun/Tun/Uinal/Kin
  • Tzolkin Cycle: Modulo 260 arithmetic for sacred calendar dates
  • Haab Solar Year: 365-day cycle with 5-day Wayeb period