Interactive Mayan Long Count Calculator: Step-by-Step Conversions & Examples

Interactive Mayan Long Count Calculator: Step-by-Step Conversions & Examples

The Mayan Long Count is a non-repeating calendar system used by the ancient Maya to record absolute dates. An interactive Mayan Long Count calculator helps convert between Gregorian dates and Long Count notation (baktun.katun.tun.uinal.kin) and visualize how the Long Count components map to our calendar. This article explains the Long Count, walks through step-by-step conversions, and gives examples you can follow using an interactive tool.

What is the Mayan Long Count?

• Structure: The Long Count expresses days since a fixed starting point (usually 0.0.0.0.0). Its five place values are:
  • Baktun = 144,000 days (20 × 20 × 18 × 20)
  • Katun = 7,200 days (20 × 18 × 20)
  • Tun = 360 days (18 × 20)
  • Uinal = 20 days
  • Kin = 1 day
• Epoch: The conventional correlation places 0.0.0.0.0 at Gregorian 3114 BCE August 11 (the GMT correlation — 584,283 days before the Gregorian epoch). Minor correlation variants exist, but GMT is the most commonly used.
• Notation: A Long Count date is written as baktun.katun.tun.uinal.kin (e.g., 13.0.0.0.0).

How an interactive calculator works

An interactive Long Count calculator typically:

1. Accepts a Gregorian date (year, month, day) or a Long Count string.
2. Converts the Gregorian date to a Julian Day Number (JDN) or computes days since the Mayan epoch using the chosen correlation constant.
3. Decomposes the total day count into Long Count place values (baktun, katun, tun, uinal, kin).
4. Displays the result and may show intermediate values, visual timelines, or reverse conversions.

Step-by-step conversion: Gregorian → Long Count

Assuming the GMT correlation (constant = 584,283 days):

1. Convert the Gregorian date to Julian Day Number (JDN).
   • Use a standard algorithm (e.g., Fliegel–Van Flandern) to compute JDN for the given year, month, day.
2. Compute days since Mayan epoch:
   • days = JDN − 584,283
3. If days is negative, you still can compute the Long Count (it yields dates before the epoch).
4. Decompose days into Long Count units:
   • baktun = floor(days / 144