Free Mayan Long Count Calculator: Find Tzolkin, Haab & Long Count DatesThe Maya developed one of the most sophisticated calendar systems in the ancient world. At its core are three complementary components: the Long Count, which records linear days over many centuries; the Tzolk’in, a 260-day ritual cycle; and the Haab’, a 365-day solar-style year. A free Mayan Long Count calculator brings these systems together, allowing you to convert modern Gregorian dates into their corresponding Maya calendar equivalents and explore how the cycles interlock.
What the Calculator Does
A good free Mayan Long Count calculator will:
- Convert any Gregorian date (including historical dates and modern dates) into a Long Count representation (baktun.katun.tun.uinal.kin).
- Provide the corresponding Tzolk’in date: a number (1–13) paired with one of 20 day names (e.g., 4 Ajaw).
- Provide the corresponding Haab’ date: a number (0–19 for months) and one of 18 month names plus the 5-day Wayeb’ period (e.g., 3 K’ank’in).
- Display the Julian Day Number (JDN) used for internal calculations and optionally show intermediate steps (day counts, offsets).
- Handle BCE dates where possible and indicate any limitations for very ancient or ambiguous historical calendar correlations.
Background: How the Maya Counted Time
The Long Count is a vigesimal (base-20) system modified to fit the solar year. Its units are:
- 1 kin = 1 day
- 1 uinal = 20 kins = 20 days
- 1 tun = 18 uinals = 360 days
- 1 katun = 20 tuns = 7,200 days
- 1 baktun = 20 katuns = 144,000 days
A Long Count date is typically written as five numbers separated by periods, for example 13.0.0.0.0, which marks a significant cycle completion.
The Tzolk’in combines 13 numbers with 20 day names to produce a 260-day cycle. The Haab’ is a 365-day cycle composed of 18 months of 20 days plus a 5-day unlucky period called Wayeb’.
The Correlation Problem (and the GMT Correlation)
Converting between Gregorian and Maya calendars requires aligning them with a chosen correlation constant—an offset that maps a known Long Count date to a Julian Day Number. The most widely accepted correlation is the Goodman–Martinez–Thompson (GMT) correlation, which sets the base date:
- GMT correlation: Long Count 0.0.0.0.0 = JDN 584,283 = August 11, 3114 BCE (proleptic Gregorian)
Your calculator should state which correlation it uses (GMT is standard), and ideally allow advanced users to select alternatives.
How Conversions Work (Overview)
- Convert the given Gregorian date to its Julian Day Number (JDN).
- Subtract the correlation constant (e.g., 584,283) to get the number of days since Long Count 0.0.0.0.0.
- Decompose that day count into baktuns, katuns, tuns, uinals, and kins using the Long Count unit values.
- For Tzolk’in: calculate the position in the 260-day cycle (number = ((day count + 4) mod 13) + 1; name index = ((day count + 19) mod 20) assuming a known alignment).
- For Haab’: compute position in the 365-day cycle (month/day = (day count + 348) mod 365), mapping into 18 months of 20 days plus the 5-wayeb days.
(Exact offsets vary slightly depending on the correlation and naming conventions; the calculator should document the formulas it uses.)
Features to Look for in a Free Calculator
- Clear indication of the correlation constant used (GMT or alternatives).
- Support for BCE/proleptic Gregorian dates and dates far in the future.
- Display of Long Count, Tzolk’in, Haab’, and JDN.
- Option to show calculation steps for learning or verification.
- Batch conversion capability (CSV upload/download).
- Mobile-friendly UI and copy/export buttons for results.
- Explanatory tooltips for Maya terms (baktun, katun, tun, uinal, kin, Wayeb’, etc.).
Example Conversions
Using the GMT correlation and proleptic Gregorian calendar:
- Gregorian 2012-12-21 → Long Count 13.0.0.0.0, Tzolk’in 4 Ajaw, Haab’ 3 K’ank’in.
- Gregorian 2025-08-29 → Long Count and cycles can be computed by the calculator to show current Maya dates.
A free calculator will reproduce these results instantly and show the intermediate JDN and day counts.
Implementing a Simple Calculator (Algorithm Outline)
- Step 1: Compute JDN from Gregorian date (standard algorithm).
- Step 2: dayCount = JDN – correlationJDN.
- Step 3: Compute Long Count:
- baktun = floor(dayCount / 144000)
- remainder = dayCount % 144000
- katun = floor(remainder / 7200)
- remainder %= 7200
- tun = floor(remainder / 360)
- remainder %= 360
- uinal = floor(remainder / 20)
- kin = remainder % 20
- Step 4: Compute Tzolk’in and Haab’ using modular arithmetic with documented offsets.
- Step 5: Format and present results.
Use Cases
- Scholars and students studying Maya history and inscriptions.
- Enthusiasts exploring correlations between modern dates and Maya cycles.
- Developers building educational tools, exhibits, or interactive timelines.
- Genealogists or historians verifying dates in colonial-era documents that reference Maya dates.
Caveats & Historical Notes
- The GMT correlation is widely accepted but not universally agreed upon; alternative correlations exist and can shift results by days.
- The Maya used regional and temporal variations; inscriptions sometimes reflect local counting habits.
- Proleptic Gregorian conversions for very ancient dates assume the Gregorian calendar extended backward; historians sometimes prefer Julian calendar dates in some contexts.
Where to Try One
Look for academic websites, university tools, museum pages, or open-source calculators that state their correlation and provide transparent calculations. Many free tools also offer downloadable conversion tables or APIs for integration.
If you want, I can:
- provide code (JavaScript or Python) for a working Long Count/Tzolk’in/Haab’ converter, or
- generate a CSV of sample conversions for a range of years.
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