How this calculator works
The Long Count is a tally of days from 11 August 3114 BCE in the proleptic Gregorian calendar, built from five places: baktun (144,000 days), katun (7,200), tun (360), winal (20) and kin (1). The starting date 0.0.0.0.0 corresponds to Julian day number 584,283 in the GMT correlation used here, and the well-known 13.0.0.0.0 falls on 21 December 2012. Alongside the Long Count run two independent cycles. The Tzolkin combines a number from 1 to 13 with one of twenty day names, repeating every 260 days, and the Haab is a 365-day year of eighteen twenty-day months plus a five-day Wayeb period.
Formula
days since 0.0.0.0.0 = baktun x 144000 + katun x 7200 + tun x 360 + winal x 20 + kin. Tzolkin number = ((days + 3) mod 13) + 1, with the day name at index (days + 19) mod 20. Haab position = (days + 347) mod 365, with month = floor(position / 20) and day = position mod 20 + 1, or the Wayeb when month is 18.
Worked example
The Long Count 13.0.0.0.0 is 13 x 144,000 = 1,872,000 days from the start, which is 21 December 2012. On that day the Tzolkin is 4 Ajaw and the Haab is 3 Kankin. The Gregorian date 1 January 2000 corresponds to 12.19.6.15.2, which is 11 Ik in the Tzolkin and 10 Kankin in the Haab. Converting those back through the same correlation returns 1 January 2000.
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Frequently asked questions
Why use the 584283 correlation?
Several correlations map the Long Count onto the Julian day count. The 584283 value is the most widely used because it places the 13.0.0.0.0 cycle end on 21 December 2012, a date widely popularised. Other scholars prefer slightly different values, which can shift results by a few days.
What is the Tzolkin?
It is a 260-day ritual calendar made of a number cycle of 13 and a name cycle of 20. The two cycles mesh so that a combination repeats only every 260 days, and it was used for divination and naming.
What is the Haab?
It is the 365-day solar year of eighteen twenty-day months plus Wayeb, five days considered unlucky. It drifts against the true solar year because it has no leap day.
Does the Long Count really end in 2012?
No. 13.0.0.0.0 completed the thirteenth baktun and the count continued to 14.0.0.0.0 and beyond. The 2012 date marked a cycle boundary, not the end of the calendar.