# Maya Calendar Conversions - Calendar Conversions: Example 2

Author(s):
Ximena Catepillan (Millersville University of Pennsylvania) and Waclaw Szymanski (West Chester University of Pennsylvania)

Figure 5: Millersville University student Kaleena Rodriguez in Coba, Mexico, 2006 (Photo by Ximena Catepillán.)

The Long Count date 8. 14. 3. 1. 12 (8 baktuns, 14 katuns, 3 tuns, 1 uinals, 12 kins) is carved in the Leyden Plaque.  This plaque, a jade pendant, has the shape of a miniature stela with a human figure in the front and a long count date in the back. It is possible that the plaque is originally from Tikal.

Figure 6:  Ximena Catepillán holding a replica of the Leyden Plaque at a store in Valladolid, Mexico, 2009 (Photo by Alejandra Merino Trujillo.)

a)  Compute the number of kins (K).

 Baktun: 8 x 144,000 = 1,152,000 Katun: 14 x 7,200 = 100,800 Tun: 3 x 360 = 1,080 Uinal: 1 x 20 = 20 Kin: 12 x 1 = 12 Total: K = 1,253,912

b)  Now we divide K by 18,980 to determine the number of full Round Calendar cycles that elapsed up to K, and, more importantly, to find the remainder, which gives the location of the date within one Round Calendar cycle:

1,253,912/18,980 = 66 + 1,232/18980. This means that 66 Round Calendar cycles elapsed and the date we seek is the 1,232nd kin or day from the starting date of 4 Ahau 8 Cumku in the Round Calendar cycle. Let R = 1,232.

c)  Now we will determine the Tzolkin date. To do this we divide R by 13 and by 20:

1,232/13   = 94 + 10/13

1,232/20   = 61 + 12/20.

This means that 1,232 days consist of 94 13-day cycles, plus A = 10 extra days, and also of 61 20-day cycles of gods, plus B = 12 extra gods.  Since the Tzolkin date for the beginning of the Maya world was 4 Ahau, we add 10 days to 4 days, which gives 14.  But there are only 13 day numbers in the Tzolkin calendar, so our Tzolkin number is 1.  To see this, we imagine the numbers 1 through 13 on a circle (like the numbers 1 through 12 on a clock face).  If we begin at 4 and move 10 days forward, we will end at 1.  Another way to say this is to say that 14 modulo 13 is 1. To find the appropriate god, we advance 12 steps clockwise (mod 20) from Ahau around the Tzolkin 20-cycle to the god Eb.  Therefore the Tzolkin date is 1 Eb.

Figure 7:  The Tzolkin 20-cycle  (Robinson 2002)

d)  To determine the Haab Calendar date we begin by dividing R by 365, the number of days in the Haab calendar:

1,232/365 = 3 + 137/365.

This means that 1,232 days consist of 3 365-day Haab Calendar cycles, plus H = 137 extra days.  The day we seek is the 137th day from the starting date of 8 Cumku in the Haab Calendar cycle.  As previously noted, since 17 ≤ H ≤ 364, the Haab Calendar date we seek falls between 0 Pop and 7 Cumku (inclusive).  If we replace the remainder H by H’ = H – 17 = 137 – 17 = 120, the day we seek is the 120th day from the date 0 Pop in the Haab Calendar.

Next we divide H’ = 120 by 20, the number of days per month (or god) in the Haab Calendar:

120/20 = 6 + 0/20.

This means exactly 6 20-day months have passed since 0 Pop.  If we count 6 gods forward from Pop, we find the god Yaxkin.  Therefore, the Haab Calendar date is 0 Yaxkin.

Figure 8: The Haab 18-month name glyphs and the Uayeb (Aveni 1980)

e)  We conclude that the Round Calendar Date is 1 Eb 0 Yaxkin.

Ximena Catepillan (Millersville University of Pennsylvania) and Waclaw Szymanski (West Chester University of Pennsylvania), "Maya Calendar Conversions - Calendar Conversions: Example 2," Convergence (October 2010), DOI:10.4169/loci003536