- Maya time relied on the counting of completed days.
- They used a number system based on the vigesimal (base 20) system of counting.
- There are two types of glyph;
- those that are found on concertina like books known currently as codices (plural of codex) and
- those on carved or moulded stelae and architecture.

- Time zero begins on a date known as 4 Ahau 8 Cumhu

1 day = 1 Kin 20 days = 20 Kin = 1 Uinal 360 " = 18 Uinal = 1 Tun = 1 year approximately 7 200 " = 20 Tun = 1 Katun = 20 years " 144 000 " = 20 Katun = 1 Bactun = 395 " " 2 880 000 " = 20 Bactun = 1 Pictun, = 7 885 " " 57 600 000 " = 20 Pictun = 1 Kinchiltun = 157 703 " " 115 200 000 " = 20 Kinchiltun = 1 Alautun = 3 154 069 " "

But, they rarely used Pictun, Kinchiltun and Alautun depictions. Their usual calculations mostly concerned terms up to Baktun, since 8000 years would be a significantly broad enough time to consider.

Glyph Type | Codex Type | Numeral |
---|---|---|

1 | ||

2 | ||

3 | ||

4 | ||

5 | ||

6 | ||

7 | ||

8 | ||

9 | ||

10 | ||

11 | ||

12 | ||

13 | ||

14 | ||

15 | ||

16 | ||

17 | ||

18 | ||

19 | ||

0 | ||

(Codex glyph only) | 0 |

Mayan numerals come in several forms. In the codices, they are usually written in columns, with the Kin value lowermost and successively greater time periods above. The relative positions of these are sufficient to show the time recorded. These numerals are black if they are positive in value, whilst red, if they must be the number need to subtract from the black numerical value of time in days.

For glyphic representation on monuments and stelae, they are carved in the vertical form. However, there are also head variants which represent numerals. These are sadly lacking in some of the sequence, so they have not been included here. Only the zero half-flower is shown.

Codex Glyph | Name | Meaning |
---|---|---|

Imix | Water, Wine, Sea Dragon | |

Ik | Air, Life | |

Akbal | Night | |

Kan | Corn | |

Chicchan | Serpent | |

Cimi | Death | |

Manik | Deer, grasp | |

Lamat | Rabbit | |

Muluc | Rain | |

Oc | Dog | |

Chuen | Monkey | |

Eb | Broom | |

Ben | Reed | |

Ix | Tiger, Magician | |

Men | Bird, Eagle, Wise One | |

Cib | Owl, Vulture | |

Caban | Force, Earth | |

Eznab | Flint Knife | |

Cauac | Storm, Tun | |

Ahau | Lord |

Stelae Glyphs | Name | Meaning |
---|---|---|

Pop | Mat | |

Uo | Frog | |

Zip | Stag | |

Zotz | Bat | |

Tzec | Skull | |

Xul | Termination | |

Yaxkin | Red | |

Mol | To Gather | |

Chen | A Well | |

Yax | Green | |

Sac | White | |

Ceh | A Forest | |

Mac | A Cover | |

Kankin | Yellow, Skeleton, Ribs | |

Muan | Falcon, An Owl | |

Pax | A Drum | |

Kayab | Turtle | |

Cumhu | Dark | |

Uayeb | A Ghost |

0 Pop 1 st day of the Haab 1 Pop 2 nd " " " " 2 Pop 3 rd " " " " 3 Pop 4 th " " " " 4 Pop 5 " " " " " 5 Pop 6 " " " " " 6 Pop 7 " " " " " 7 Pop 8 " " " " " 8 Pop 9 " " " " " 9 Pop 10 " " " " " 10 Pop 11 " " " " " 11 Pop 12 " " " " " 12 Pop 13 " " " " " 13 Pop 14 " " " " " 14 Pop 15 " " " " " 15 Pop 16 " " " " " 16 Pop 17 " " " " " 17 Pop 18 " " " " " 18 Pop 19 " " " " " 19 Pop 20 " " " " " 0 Uo 21 st " " " " 1 Uo 22 nd " " " " 2 Uo 23 rd " " " " 3 Uo 24 th " " " " . . 18 Cumhu 359 " " " " " 19 Cumhu 360 " " " " " 0 Uayeb 361 st " " " " 1 Uayeb 362 nd " " " " 2 Uayeb 363 rd " " " " 3 Uayeb 364 th " " " " 4 Uayeb 365 " " " " "

1 Imix 1 st day of the Tzolkin 2 Ik 2 nd " " " " 3 Akbal 3 rd " " " " 4 Kan 4 th " " " " 5 Chicchan 5 " " " " " 6 Cimi 6 " " " " " 7 Manik 7 " " " " " 8 Lamat 8 " " " " " 9 Muluc 9 " " " " " 10 Oc 10 " " " " " 11 Chuen 11 " " " " " 12 Eb 12 " " " " " 13 Ben 13 " " " " " 1 Ix 14 " " " " " 2 Men 15 " " " " " 3 Cib 16 " " " " " 4 Caban 17 " " " " " 5 Eznab 18 " " " " " 6 Cauac 19 " " " " " 7 Ahau 20 " " " " " 8 Imix 21 st " " " " 9 Ik 22 nd " " " " 10 Akbal 23 rd " " " " 11 Kan 24 th " " " " 12 Chicchan 25 " " " " " 13 Cimi 26 " " " " " 1 Manik 27 " " " " " 2 Lamat 28 " " " " " 3 Muluc 29 " " " " " 4 Oc 30 " " " " " 5 Chuen 31 st " " " " 6 Eb 32 nd " " " " 7 Ben ... 33 rd " " " " . . 7 Imix 241 st " " " " 8 Ik 242 nd " " " " 9 Akbal 243 rd " " " " 10 Kan 244 th " " " " 11 Chicchan 245 " " " " " 12 Cimi 246 " " " " " 13 Manik 247 " " " " " 1 Lamat 248 " " " " " 2 Muluc 249 " " " " " 3 Oc 250 " " " " " 4 Chuen 251 st " " " " 5 Eb 252 nd " " " " 6 Ben 253 rd " " " " 7 Ix 254 th " " " " 8 Men 255 " " " " " 9 Cib 256 " " " " " 10 Caban 257 " " " " " 11 Eznab 258 " " " " " 12 Cauac 259 " " " " " 13 Ahau 260 " " " " "

These are the twenty daynames of the Maya 'week'. The term week is applied loosely, and corresponds to the same idea as Monday, Tuesday.....Sunday does in the Western Calendar. Like the Western Calendar, the 20 daynames are cyclic, that is, they repeat again and again each in sequence. Their names are, Imix, Ik, Akbal, Kan, Chicchan, Cimi, Manik, Lamat, Muluc, Oc, Chuen, Eb, Ben, Ix, Men, Cib, Caban, Etznab, Cauac, Ahau. These are but stylised glyphs taken from codex representations. There are a whole separate grouping of glyphs which are found only in stone and stucco stelae.

Glyph | Name |
---|---|

Kin | |

Uinal | |

Tun | |

Katun | |

Bactun | |

Pictun | |

Kinchiltun | |

Alautun |

These calendrical symbols are based in part to the Mayan vegesimal system of counting. The basic unit of astronomic calculations is the day, or Kin. 20 Kin = 1 Uinal. Next, a break from the vegesimal system occurs, with 18 Uinal = 360 Kin = 1 Tun. 20 Tun = 1 Katun, 20 Katun = 1 Bactun, 20 Bactun = 1 Pictun, 20 Pictun = 1 Kinchiltun, 20 Kinchiltun = 1 Alautun. These are stelae and stucco glyphs from various buildings.

But, they rarely used Pictun, Kinchiltun and Alautun depictions. Their usual calculations mostly concerned terms up to Baktun, since 8000 years would be a significantly broad enough time to consider.

We can demonstrate this by the following, the start and end of a Calendar Round.

============================= ==================== =================== ========== Day of the Tzolkin Day of the Haab Calendar Round Date Day Number ============================= ==================== =================== ========== Day 1 of the 1st Tzolkin; Day 1 of 1st Haab = 1 IMIX 0 POP = DAY 1 Day 2 of the 1st Tzolkin; Day 2 of 1st Haab = 2 IK 1 POP = DAY 2 Day 3 of the 1st Tzolkin; Day 3 of 1st Haab = 3 AKBAL 2 POP = DAY 3 Day 4 of the 1st Tzolkin; Day 4 of 1st Haab = 4 KAN 3 POP = DAY 4 Day 5 of the 1st Tzolkin; Day 5 of 1st Haab = 5 CHICCHAN 4 POP = DAY 5 Day 6 of the 1st Tzolkin; Day 6 of 1st Haab = 6 CIMI 5 POP = DAY 6 Day 7 of the 1st Tzolkin; Day 7 of 1st Haab = 7 MANIK 6 POP = DAY 7 Day 8 of the 1st Tzolkin; Day 8 of 1st Haab = 8 LAMAT 7 POP = DAY 8 Day 9 of the 1st Tzolkin; Day 9 of 1st Haab = 9 MULUC 8 POP = DAY 9 Day 10 of the 1st Tzolkin; Day 10 of 1st Haab = 10 OC 9 POP = DAY 10 Day 11 of the 1st Tzolkin; Day 11 of 1st Haab = 11 CHUEN 10 POP = DAY 11 Day 12 of the 1st Tzolkin; Day 12 of 1st Haab = 12 EB 11 POP = DAY 12 Day 13 of the 1st Tzolkin; Day 13 of 1st Haab = 13 BEN 12 POP = DAY 13 Day 14 of the 1st Tzolkin; Day 14 of 1st Haab = 1 IX 13 POP = DAY 14 Day 15 of the 1st Tzolkin; Day 15 of 1st Haab = 2 MEN 14 POP = DAY 15 Day 16 of the 1st Tzolkin; Day 16 of 1st Haab = 3 CIB 15 POP = DAY 16 Day 17 of the 1st Tzolkin; Day 17 of 1st Haab = 4 CABAN 16 POP = DAY 17 Day 18 of the 1st Tzolkin; Day 18 of 1st Haab = 5 EZNAB 17 POP = DAY 18 Day 19 of the 1st Tzolkin; Day 19 of 1st Haab = 6 CAUAC 18 POP = DAY 19 Day 20 of the 1st Tzolkin; Day 20 of 1st Haab = 7 AHAU 19 POP = DAY 20 Day 21 of the 1st Tzolkin; Day 21 of 1st Haab = 8 IMIX 0 UO = DAY 21 Day 22 of the 1st Tzolkin; Day 22 of 1st Haab = 9 IK 1 UO = DAY 22 Day 23 of the 1st Tzolkin; Day 23 of 1st Haab = 10 AKBAL 2 UO = DAY 23 Day 24 of the 1st Tzolkin; Day 24 of 1st Haab = 11 KAN 3 UO = DAY 24 Day 25 of the 1st Tzolkin; Day 25 of 1st Haab = 12 CHICCHAN 4 UO = DAY 25 . . Day 253 of the 73rd Tzolkin; Day 358 of 52nd Haab = 6 CIB 16 CUMHU = DAY 18973 Day 254 of the 73rd Tzolkin; Day 359 of 52nd Haab = 7 CIB 17 CUMHU = DAY 18974 Day 255 of the 73rd Tzolkin; Day 360 of 52nd Haab = 8 CIB 18 CUMHU = DAY 18975 Day 256 of the 73rd Tzolkin; Day 361 of 52nd Haab = 9 CIB 19 CUMHU = DAY 18976 Day 257 of the 73rd Tzolkin; Day 362 of 52nd Haab = 10 CABAN 1 UAYEB = DAY 18977 Day 258 of the 73rd Tzolkin; Day 363 of 52nd Haab = 11 EZNAB 2 UAYEB = DAY 18978 Day 259 of the 73rd Tzolkin; Day 364 of 52nd Haab = 12 CAUAC 3 UAYEB = DAY 18979 Day 260 of the 73rd Tzolkin; Day 365 of 52nd Haab = 13 AHAU 4 UAYEB = DAY 18980 ============================= ==================== =================== ========== Day of the Tzolkin Day of the Haab Calendar Round Date Day Number ============================= ==================== =================== ========== This gives 18980 unique Calendar Round dates.

The right most numeral represents the Kin value. Here we have 4 Kin. Next to the left, is the number of Uinals in this date, 6 and so on. The following gives the calculation of the total number of days in arabic numerals of the vigesimal Mayan date 9.15.2.6.4 :

1 day x 4 Kin = 4 20 days x 6 Uinal = 120 360 " x 2 Tun = 720 7 200 " x 15 Katun = 108000 144 000 " x 9 Bactun = 11664000 ====================================================== Total number of days is 11772844 days

The total number of days 11772844 must first be divided by 13, and find the remainder.

11772844 divided by 13 is 905603 with a remainder of 5.

Next, the total number of days 11772844 must first be divided by 20, and find the remainder.

11772844 divided by 20 is 588642 with a remainder of 4.

The use of the remainders will give us the necesary information on how to advance the Tzolkin part of the zero date 4 Ahau, to the sample date 9.15.2.6.4.

Add the first remainder, 5, to 4 (of 4 Ahau). This gives 9. If the result is greater than 13, then all multiples of 13 must be taken to give a remainder. Since our result is 9, we proceed to the next part.

This involves advancing daynames forward from Ahau by the number of days given by the second remainder, 4. This would lead us to Kan.

So the Tzolkin part of the date is 9 Kan.

11772844 divided by 365 is 32254 with a remainder of 134.

Hence 134 days must be advanced from the Haab date 8 Cumhu.

Since Cumhu is the 18th month, 8 Cumhu is the ninth day. Since there are 20 days in this month, there are 11 remaining plus the five of the Uayeb month. This makes 16 days. Subtracting 16 from 134 leaves 118 days. This has 5 completed months of 20 days, and 18 days into the sixth month. The Haab date is therefore 17 Xul.

| Typical Codex column representation of 9.15.2.6.4 |
---|

The Tzolkin and Haab dates and the numeral values of the time periods can be used to check if the the calculations are correct.

© Dylan W.H.Sung 1996-onwards

This page was created on Sunday 24th May 1998. It was recently updated on Monday 22nd April 2002