# Mayan Calendar Converter

Created by Davide Borchia
Reviewed by Anna Szczepanek, PhD and Rijk de Wet
Last updated: Jan 18, 2024

K'ank'in and Muwan instead of January and July: learn how to write any date the Mayan way with our Mayan calendar converter!

Here you will learn a lot of things! Starting from briefly explaining what the Mayan calendar is, we will teach you its elements and their meaning. Then, you will learn how to read the Mayan calendar and write a "modern" date the old way. We will answer your questions too: when did the Mayan calendar start and end? How far does the Mayan calendar go?

## Who were the Mayans?

Well before Europeans discovered — and conquered — the Americas, numerous civilizations were flourishing there: among them, the Maya civilization was undoubtedly the most developed, with traces dating back ten thousand years and evidence of a millennium-long culture.

Renowned for their exquisite mathematical skills, Mayans had a passion for calculating things (they would still use omnicalculator, though!). They were able to finely predict the movements of planets through the occurrence of eclipses, for example. They loved to count using their numerals: we found them so amazing that we made a calculator to teach you to do the same: try our Mayan numerals converter!

🔎 We know how to read the Mayan inscriptions thanks to an interesting ethnographer: Yuri Knorozov. The Soviet researcher embarked on the difficult task of deciphering the Mayan scripts, eventually succeeding. However, he could visit the archeological sites only years after his success.

To keep track of the vast number of celebrations, rituals, and astronomical events, the Mayans needed a calendar, and boys, which calendar they developed!

## An overview: the Mayan calendar explained

For starters, forget your everyday calendar! We will dive deeply in a complex way to represent dates, including cycles, creation dates, and unlucky days. Ready?

There are different ways to uniquely identify a date using the Mayan calendar, differing in the amount of time required to cycle through an entire "year". From the shortest to the longest, we meet:

• The Tzolk'in calendar;
• The Haab calendar; and
• The Mayan long count calendar.

An additional calendar is connected to the underworld deities: the Lord of the Nights.

We will analyze all of them, one after the other!

## The Mayan calendar Tzolk'in

Let's learn how to count in the first of the Mayan calendars. The Tzolk'in calendar describes the Mayan sacred round, a 260 days calendar obtained by repeating a set of 20 days' names. We list them below, with the order represented by the numbers in the Order column.

Order

Name

Order

Name

01

Imix

11

Chuwen

02

Ik'

12

Eb'

03

Ak'b'al

13

B'en

04

K'an

14

Ix

05

Chikchan

15

Men

06

Kimi

16

K'ib'

07

Maink'

17

Kab'an

08

Lamat

18

Etz'nab'

09

Muluk

19

Kawak

10

Ok

20

Ajaw

Each day is numbered from 1 to 13, starting from Imix. When we reach the number 13, we start counting again from 1, like this:

Number

Name

01

Imix

02

Ik'

03

Ak'b'al

...

12

Eb'

13

B'en

01

Ix

02

Men

...

This mechanism allows generating 13×20 = 260 unique combinations of numbers and days.

🔎 This is the first appearance of the number 20 in our Mayan calendar converter: however, you will see it on many other occasions! Mayan had a deep relationship with that number: for instance, their numerical system was vigesimal, which means it used base 20.

🔎 Our numeral system is in base 10 — that's why it is called decimal. There are many other bases: binary, octal, hexadecimal.... discover them all with our tools!

Admittedly, the Tzolk'in calendar is uncommon in its length: it doesn't share the length of any astronomical phenomenon. Its origins are still debated. We know that 20 was an important number for the Mayans (you have 20 fingers and toes); for 13 we need to refer to the Mayan religion, where 13 is the number of levels of the Upperworld (the residence of Mayan gods). Maybe that's the origin, maybe it's not — we'd have to ask a Mayan to be sure.

260 is the approximate duration in days of a human pregnancy and the duration of a crop cycle of maize. It is possible that for the Mayans, the Tzolk'in calendar was an "Earthly" calendar, not connected to the skies.

The Tzolk'in calendar is still used, and many traditions make extensive references to this cycle.

Parents can choose the name of their children according to specific combinations of numbers and days, for example. Other combinations are deemed inauspicious for events such as weddings.

## The Mayan calendar Haab

The Haab calendar is the next one on the list. You can finally see an astronomical connection with this one, but let's start from the basis!

The Haab calendar resembles more closely the Gregorian calendar. Two numbers define it:

• 18 months; and
• 20 days per month.

We're sure you spotted it: there's 20 again. Let's check out the name of the months!

Id

Name

Id

Name

01

Pop

10

Yax

02

Wo'

11

Sak'

03

Sip

12

Keh

04

Sotz'

13

Mak

05

Sek

14

K'ank'in

06

Xul

15

Muwan

07

Yaxk'in

16

Pax

08

Mol

17

K'ayab'

09

Ch'en

18

Kumk'u

There are then 20×18 = 360 unique combinations of day's number and month, which brings the duration of a Haab year close to the revolution period of Earth. But where are the 5 (or, from time to time, 6) days to reach our familiar 365? We're glad you asked!

Mayans introduced an extra "month" lasting only five days. Its name is wayeb', and Mayans traditionally associated it with bad luck.

🔎 Mayans were definitely smart, and they didn't ignore the actual duration of the year (~365.25 days): they smoothly ignored it, merely noting that there was a discrepancy between the Haab calendar and the Solar cycle. No leap years in the Mayan calendar!

To obtain a Haab date, you follow a familiar scheme of numbered days in each month: you start at 1, and when you reach 20, you begin the next month. No different lengths and no "Thirty Days Hath September"!

## The long count Mayan calendar

Combining Tzolk'in and Haab calendars gives you a cycle of about 52 years of uniquely identified dates. Apparently, for Mayans, this was not enough: we need to introduce the long count.

The long count calendar is a hierarchy of time periods that repeats over more than five thousand years. Starting from the shortest element of the calendar, we meet:

• K'in, which equals 1 day;
• Uinal, corresponding to 20 k'in;
• Tun, which contains 18 uinal;
• K'atun, corresponding to 20 tun;
• B'ak'tun, made of 20 k'atun.

The number of days in each "unit" increases, from 360 in a single tun to 144,000 in a b'ak'tun. This value corresponds to almost four centuries (394 years).

The long count calendar doesn't stop here: after b'ak'tun, there are other multiples of 20, like the piktun. However, they change so rarely that it's effectively useless to include them in the calculations.

The current piktun started on a precise day, the 11ᵗʰ of August, 3114 BCE. In Mayan theology, that day corresponds to the creation day. The first piktun will end in more about 3,000 years. In writing a long count date, we then consider only the smaller elements: they are written from left to right, the longest element first, and separated by points:

(b'ak'tun).(k'atun).(tun).(uinal).(k'in)

The creation day corresponds to 0.0.0.0.0, and the dates grow from there.

## The Lords of the Night

It''s not over yet! There's another date identifier in the Mayan calendar: the Lord of the Night. This calendar is the easiest one to understand: it consists of a succession of nine gods, starting from the last one on the creation day.

In a complete Mayan date, the Lord of the Night is identified by the letter G, followed by a number between 1 and 9.

The names of the Lord of the Nights are:

Id

Name

Meaning

1

Xiuhtecuhtli

Fire Lord

2

Texcatlipoca

Smoking mirror

3

Piltzintecuhtli

Prince Lord

4

Centeotl

Maize God

5

Mitlantecuhtli

Underworld Lord

6

Chalchiuhtlicue

7

Tlazolteotl

Filth God

8

Tepeyollotl

Mountain heart

9

Tlaloc

Rain God

## The Mayan calendar symbols

Mayans didn't use numbers or names exclusively in their calendars — they used a set of glyphs, each of them associated with specific elements (days, months, k'atun...). There were a lot of symbols: deciphering them took a lot of time, but it helped historians understand the Mayan calendar so well that we could create this calculator.

## How to convert a date to the long count calendar?

You have to trust us this time: calculating a date in the Mayan calendar is complicated, and it's better to leave the task to our calendar converter. However, we will give you some general indications.

We will cover the main steps:

• Convert a Gregorian date to the Julian day number (JDN);
• Gradually calculate the elements of the long count date;
• Identify the Tzolk'in date; and
• Identify the Haab date.

⚠️ When talking about dates, we will use the format dd/mm/yyyy!

The Julian day number (JDN) is the number of days between a specific date and the 1ˢᵗ of January, 4713 B.C.E., the starting date of this numeration system. The currents JDNs are pretty high as a consequence, but it's not a big deal: they are primarily used by historians and astronomers, and we are sure they can handle them!

🔎 The starting date of the JDN falls on the "intersection" of three calendars system: the solar cycle, the Metonic cycle (related to lunar phases), and the indiction cycle (a Roman taxation calendar). It's not a coincidence that the 1ˢᵗ of January 4713 BC was a Monday!

You have to apply a to convert from the Gregorian calendar (the one used worldwide) to the JDN. We will do it for you in our Mayan calendar converter!

Here are some examples:

$\footnotesize \begin{split} 20/07/1969\ \text{AD}&\rightarrow 2,\!440,\!423 \\ 22/10/1454\ \text{AD}&\rightarrow 2,\!252,\!417\\ 21/04/753\ \text{BC} &\rightarrow 1,\!446,\!508\\ 03/05/1375\ \text{BC} &\rightarrow 1,\!219,\!339 \end{split}$

We think you can guess one of them already, however, here is the list:

• Neil Armstrong takes the first step on the Moon;
• First recorded date of a printed document by Gutenberg;
• The date of the foundation of Rome, according to the legend;
• An early record of a solar eclipse in Mesopotamia.

As you can see, most of the human civilization is contained in a million days!

Now you need to find the number of days elapsed from the Mayan creation date — that's why we needed the JDN! For the creation date, we have:

$\footnotesize 11/08/3114\ \text{BC} \rightarrow 584,\!283$

This date correspond to the long count 0.0.0.0.0.

We choose a date, let's say the 17ᵗʰ of July 2021; converting it in JDN returns 2,459,413. Now consider the difference between those two dates.

$\footnotesize 2,\!459,\!413-584,\!283=1,\!875,\!130$

How many b'ak'tun does this period contain? We know the duration in days of a b'ak'tun to be 144,000: to find the number of b'ak'tun passed, we compute a simple integer division:

$\footnotesize \left\lfloor \frac{1,\!875,\!130}{144,\!000} \right\rfloor=13$

So, 13 is the number of b'ak'tun, and the beginning of the long count date. To proceed with the calculation, we take the remainder of the same operation: in the following steps it will give us the number of the next "period".

$\footnotesize 1,\!875,\!131\operatorname{mod}{144,\!000}=3,\!130$

Next up: the number of k'atun. Each k'atun contains 7,200 days. It's easy to see that our dates has zero ka'tun, because 7,200 doesn't fit into 3,130:

$\footnotesize \left\lfloor \frac{3,\!130}{17,\!200} \right\rfloor=0$

Our long count date now looks like "13.0".

Repeat those steps for all of the other units. For the number of the tun, we use 360 days and the same amount of days we used in the tun (since $3,130\ \operatorname{mod}\ 7,200=3,130$):

$\footnotesize \left\lfloor \frac{3,\!130}{360} \right\rfloor=8$

Which leaves us with a remainder of

$\footnotesize 3,\!130\operatorname{mod}\ 360=250$

and with our date now being "13.0.8".

Each uinal is 20 days long, which gives us the second to last element of the long count:

$\footnotesize \left\lfloor \frac{250}{20} \right\rfloor=12$

And the remainder returns the number of k'in:

$\footnotesize 250\ \operatorname{mod}\ 20=10$

Now we have the complete long count date: 13.0.8.12.10.

How to read this Mayan calendar date? 13 b'ak'tun, 0 ka'tun, 8 tun, 12 uinal and 10 k'in.

## How to calculate the rest of a Mayan calendar date: the Haab and Tzolk'in calendar

Finding the Haab and Tzolk'in part of a Mayan date is relatively easy. Knowing the Haab day and the Tzolk'in one on the creation day allows us to compute the current date by performing a simple remainder operation.

The creation date 0.0.0.0.0 coincides with Haab 8 kumk'u and Tzolk'in 4 ajaw. There is an offset we need to consider but, apart from that, the computations are no-brainers.

The Haab date is a 365-day cycle (apart from the first one after the creation day: no unlucky days for once, thus it is only 360-days long). The offset of the Haab calendar is 343 days (there are 17 days left before the beginning of the first year). Once you calculated your date difference between the current day and the Creation Day in JDN ($\text{date}_{\text{diff}}$), you can subtract 17: this aligns you with the beginning of the first Haab year. Then, compute the integer division by 365 (the duration of a full Haab year):

$\footnotesize \left\lfloor \frac{\text{date}_{\text{diff}}-17}{365} \right\rfloor$

This is the number of full Haab years elapsed since the creation date.

To find the number of days passed in the current Haab year we need to subtract from $\text{date}_{\text{diff}}$ the duration in day of the completed Haab years:

$\footnotesize \text{Haab}_{\text{date}}\!=\! \text{date}_{\text{diff}}\! -\! 365\!\cdot \!\left\lfloor \frac{\text{date}_{\text{diff}}-17}{365} \right\rfloor$

If this number is bigger than 360, your date is an unlucky day — sorry!

If not, the integer division by 20 (the length of a Haab month) will return the month, and the remainder of the same operation the day! Easy peasy Mayan squeezy!

\footnotesize \begin{align*} \footnotesize \text{Haab}_{\text{month}} & = \left\lfloor\frac{\footnotesize \text{Haab}_{\text{date}}}{20}\right\rfloor\\ \\ \footnotesize \text{Haab}_{\text{day}}&=\footnotesize \text{Haab}_{\text{date}}\ \text{mod}\ 20 \end{align*}

The reasoning behind the Tzolk'in date is similar. In this case, the year "0" starts at day number 159: this is our new offset. Subtract that number from $\text{date}_{\text{diff}}$ and take the result of the integer division by 260 (the duration of a Tzolk'in year) to find the number of completed Tzolk'in years. Now compute the day number of the current year by subtracting the date difference between the chosen date and the creation date and the number of days in the completed years:

$\footnotesize \text{Tzolk'in}_{\text{date}}\! =\!\text{date}_{\text{diff}} \!-\! 365\!\cdot \!\left\lfloor \!\frac{\text{date}_{\text{diff}}-159}{260} \!\right\rfloor$

The number and day of the Tzolk'in calendar are the remainders of the integer divisions of this number with 13 (for the number), and 20 (for the day):

\footnotesize \begin{align*} \footnotesize \text{Tzolk'in}_{\text{number}} & = \left\lfloor\frac{\footnotesize \text{Tzolk'in}_{\text{date}}}{13}\right\rfloor\\ \\ \footnotesize \text{Tzolk'in}_{\text{day}}&=\left\lfloor\frac{\footnotesize \text{Tzolk'in}_{\text{date}}}{20}\right\rfloor\\ \end{align*}

## How to compute the Lord of the Night?

The last part of a Mayan date is also the easiest to compute. Knowing that the creation day had Lord of the Night $\text{G}1$. From there on, using the difference between the JDN of the date and the JDN of the creation day modulo $9$ will give you the correct Lord of the Night:

$\footnotesize \text{date}_{\text{diff}}\ \text{mod}\ 9$

## How to convert a Mayan long count calendar date to a Gregorian date?

Now that you know how to convert a Gregorian date in the long count date let's try the other way round!

Take a long count date, preferably not using the Mayan calendar's symbols but numbers — unless you are in for a bit of deciphering. We chose 12.19.6.1.9.

The procedure you have to follow is straightforward. Consider the lengths of each period in the long count Mayan calendar and multiply this value for the number in the corresponding position; once you are done, sum the results together: what you find is the number of days elapsed since the Mayan creation.

\begin{align*} 12\cdot 144,000\ &+\\ 19\cdot 7,200\ &+\\ 6\cdot 360\ &+\\ 1\cdot 20\ &+\\ 9\cdot 1\ &=\\ \hline \\[-1em] 1,866,989 \end{align*}

To find the current JDN, you must add the number relative to the Mayan's creation day: 584,283.

$\footnotesize 584,\!283+1,\!866,\!989=2,\!451,\!272$

We need to apply a credited to Edward G. Richards to find the Gregorian date. We coded it in our calculator, so you don't have to worry: you will see the date in the dd/mm/yyyy format as usual!

## How to use our Mayan calendar converter?

Even if the Mayan calendar system requires a bit of work to be understood, we made a calculator as easy to use as calculating an eclipse — well, maybe slightly easier!

Choose first the "direction" of the conversion: do you want to find out today's date in the Mayan calendar or the next "end of the world"?

If you chose "Convert from..." Gregorian calendar, you can select a date from the calendar or, if you are interested in a specific day in the far future, click on Advanced mode and insert a date manually. Are you going to check your birthday in the Mayan calendar?

⚠️ Remember to use the correct format when inserting a date: dd/mm/yyyy/. Don't forget the slash at the end. If you want to insert a number before the year 0, insert the year as a negative number.

Are you looking for a conversion from the long count calendar instead? Select the appropriate conversion and insert a long count date. Remember that you have to insert five numbers, separated by periods.

Now that you know everything about Mayan calendars, why don't you check out other ancient math calculators like the Egyptian fractions calculator or the Babylonian numbers converter?

## When does the Mayan calendar end?

Yes, we were sure that this question was coming. If you were around in December 2012, then you surely remember the end-of-the-world craze.

Since you are reading this paragraph, it is clear that you survived the apocalypse, probably because it didn't happen at all. So what was all the fuss about? It was simply the end of a b'ak'tun, a sort of Mayan New Year's Eve.

Try it with our calculator: insert the fateful date of 12ᵗʰ December 2012 (write 21/12/2012/, remember the final slash): you will read 13.0.0.0.0: the first day of the 13ᵗʰ b'ak'tun!

## Lost in time

We know: understanding the Mayan calendar is not easy! That's why we created our Mayan calendar converter. We hope that reading this article helped you learn this complex topic.

Use our Mayan calendar converter to find out your birthday in the Mayan calendar, learn something new about that ancient civilization, or plan your sacrifices!

## FAQ

### How to read the Mayan calendar?

There were no numbers but symbols in the Mayan calendar! However, in the modern-day, it is more common to have the Mayan calendar explained through numbers and names. A Mayan date is composed by a set of five numbers, the long count calendar, followed by three sets of values:

• The Tzolk'in calendar, made of a combination of a number and a name;
• The Haab calendar, where you can see a day and a month; and
• The Lord of the Night, a set of nine deity marking a short week-like cycle.

### What is the Mayan calendar?

The Mayans use the Mayan calendar to keep track of time. Being highly interested in studying astronomy and accurately timing religious rituals, they used an accurate way to know the date based on not one but four calendars.

### What year is it in the Mayan calendar?

The Mayan calendar does not have "years" but elements repeating in shorter cycles. The years starting from December 2012 are in the 13ᵗʰ b'ak'tun.

### When did the Mayan calendar start and end?

The Mayan calendar has a precise start: the 11ᵗʰ of August, 3114 BC. That date corresponds to the creation day in the Mayan theology, and the long count calendar begins there with 0.0.0.0.0. There is no end in the Mayan calendar: the long count date has no boundaries! At the end of a cycle, a new one starts anew.

### How does the Mayan calendar work?

The Mayan calendar system is composed of various elements. A longer cycle, called long count, assigns a unique sequence of five numbers to each day. The Mayans added two more calendars to the long count: the Tzolk'in and the Haab, which are associated with a 280 and a 360-day cycles. Finally, a deity of the Underworld gives its name to each date in a nine-day-long cycle.

Davide Borchia
Convert from...
Gregorian calendar
Date

Long count date: 13.0.11.16.5

Tzolk'in date: 11 K'an

Haab date: 7 Ch'en

Lord of the Night: G 9 (Tlaloc)

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