Mongolian Calendar

Olli Salmi 13.3.2012 (First version uploaded 25.7.2009)

Years in the Mongolian calendar are designated by two terms, an element or colour (usually not both) and an animal. It is very easy to find these for a given Gregorian year.

1. To get the number of the element or colour subtract 3 from the year (AD) and take the last digit and find the element in the table. Odd numbers are male and even numbers female. Mongolian has a different form for the colour of female animals.
2. Next divide the same number by 12. The remainder is the number of the animal. (0=12=pig). This is easy to calculate mentally but you can deduce the remainder from the decimal part on your calculator. Add 1 to the first decimal up to .50, add 2 if its more, from .58 upwards.

Let's check the year 1192. Subtract 3 and you get 1189. The last digit is 9, so the year is black/water, male. When you divide 1189 by 12 you get 29 and a remainder of 1. So it's the year of the Black Mouse or Water Mouse.

Махбод Element Өнгө Colour

Жил Year
1 木 модон wood хөх blue
1 子鼠 хулгана mouse
2 хөхөгчин
2 丑牛 үхэр cattle
3 火 гал fire улаан red
3 寅虎 бар tiger
4 улаагчин
4 卯兔 туулай hare
5 土 шороо earth шар yellow
5 辰龙 луу dragon
6 шарагчин
6 巳蛇 могой snake
7 金 төмөр iron цагаан white
7 午马 морин horse
8 цагаагчин
8 未羊 хонин sheep
9 水 усан water хар black
9 申猴 бичин monkey
10 харагчин
10 酉鸡 тахиа fowl

11 戌狗 нохой dog

12 亥猪 гахай pig

The historical 60-year Mongolian-Tibetan cycle (жар) starts with the year of the Red Hare in 1027. To find the cycle subtract 1026 and divide by 60. The quotient indicates how many full cycles have elapsed. The next integer is the current cycle. Add 1 to the remainder to get the number of the year in the cycle.

To get the number of the year in the 60-year cycle add 12 so many times to the number of the animal cycle that the final number is the same as that of the element. For instance Water Mouse: Mouse is number 1. Add 4*12=48. The number of the year is 49. To get the Mongolian number, subtract 3 because the Mongolian cycle begins at a different point. The above table unfortunately has the Chinese order (because I didn't notice the difference when I started).

The rest of this page is under construction and reconstruction. Information is rather scarce, but in February 2012 I found information which reduces speculation. However, I'm still collecting information and links on this page, but my intention is to remove the unnecessary ones.

The Mongolian calendar is a reformed version of the Tibetan calendar, known as Төгс буянт (Tögs buyant, Very Virtuous) in Mongolian. According to Berzin and L. Terbish (Урианхан Лхасрангийн Тэрбиш) the calendar was reformed by Сүмбэ хамба Ишбалжир (Sümbe hamba Ishbaljir 1704-1788, in Tibetan Sum-pa mkhan-po Ye-shes dpal-‘byor). Years can have 353, 354, 355, 383, 384 or 385 days. The orbit of Jupiter takes 12 years (11.862 years) and Saturn 30 years (29.458).

Edward Henning has included the "New Genden Calculations" based on a work by Ye-shes dpal-‘byor in his calendar program. Unfortunately it is only for Windows, so I haven't been able to try it. However, I have managed to make a REALbasic implementation of Svante Janson's astronomical functions, so I have been able to check the epoch data for the New Genden Calculations. At present it seems very likely that they generate a correct Mongolian calendar.

The other common variants of Tibetan calendar are Phugpa, followed by the Dalai Lama, and Tsurpu.

Leap years

The Mongolian year has 12 months in common years and 13 months in leap years.
There are several lists of Mongolian New Years this is correct:

The leap years can be deduced from these lists, and they follow a simple rule. If we designate the year (AD) with Y and the remainder with R, the Mongolian leap year can be found with the formula adapted from the Islamic calendar of the Ming Dynasty [Excursus] described in Qizheng tuibu 七政推步 (1985:013-014). If the remainder R from the division [(Y+55)*24]/65 is larger than or equal to 41 (which is 65-24), the year is a leap year. The present values for New Genden calculations work correctly.

This formula for leap years works for the Phugpa calendar with the leap year determined with the formula [(Y+42)*24]/65>40.

There are other useful formulas. If Y1 and Y2 are two years (AD) the number of leap years between the beginnings of these lunar years is TRUNC((Y2*24+48)/65)-TRUNC((Y1*24+48)/65). In the common Phugpa variant of the Tibetan calendar it is TRUNC((Y2*24+57)/65)-TRUNC((Y1*24+57)/65). This formula is not normally used in Tibetan calendar calculations.

Information on dates and months has been difficult to find. Many Web sites have daily horoscopes, but often it is only possible to view the current day and there is no information open the current lunar month. The following seems to be a working version of the calendar from 2011-02-02 to 2012-02-21:
[Accessed 11.2.2012]
Days are clickable and the bottom left tells the season and the month in the cycle. There are mistakes, especially in the names of the months, so the calendar has to be taken with a grain of salt.
2011-06-29 and 2011-06-30 have switched places.
2011-07-31 starts a second Blue Sheep month (second 6th lunar month).
2011-08-30 starts a third Blue Sheep month, but 2011-09-01 is the fourth of the Red Monkey month. There are several similar inconsistencies.

For the period 2011-02-02 to 2012-02-21 the functions programmed on the basis of Svante Janson's paper work so that there are five discrepancies in dates (around the days of omitted and doubled dates). However, I believe these to be further mistakes in this online calendar, because calendars which I have printed in earlier years have no mistakes in lunar dates, even when there are other obvious mistakes, like months with the first day of the month at or near the bottom of the page.

The lunar months are not numbered, they are named with the animal cycle starting with Tiger (like in Tsurphu, and alos China). In leap years there are two months with the same name, which is very convenient since there are twelve names for twelve months. In 2011 the Iron Hare year starts with White Tiger. From this the other months can be calculated.
Lunar dates are expressed in this format:
Өвлийн дунд цагаан Хулгана сарын шинийн 9 ‘the first [day] of the middle winter month of White Tiger month’.
бар=харвын тэргүүн сар
харвын, зуны, намрын, өвлийн seasons, starting from spring, in genitive
тэргүүн, дунд, адаг (head, middle, end)

The leap month in 2011 is the month of the Blue Sheep, the 6th lunar month. The second formula in Qizheng tuibu can be adopted to calculate it. The number of the leap month is (65-R)/2. The number 2 in the formula is 24/12, the annual fraction 24/65 is divided between the months. The smaller the remainder, the later the leap month. The remainder R from [(2011+55)*24]/65=54. (65-54)/2=5.5. Rounded off this gives 6, which is the correct month, at least in this case. It would be better if some other leap months were known.

In the Phugpa tradition of Tibetan calendars the leap month and leap year is determined by what Edward Henning calls intercalation index. It is a number that increases by 2 every month and is calculated modulo 65, that is, 65 is subtracted from it if possible. Here are the intercalation indexes of three years around the epoch. A month is doubled if it has the intercalation index 48 or 49. This table is easy to make on Excel.

Months 1 2 3 4 5 6 7 8 9 10 11 12
1746 49 51 53 55 57 59 61 63 0 2 4 6
1747 8 10 12 14 16 18 20 22 24 26 28 30
1748 32 34 36 38 40 42 44 46 48 50 52 54
1749 54 56 58 60 62 64 1 3 5 7 9 11
1750 13 15 17 19 21 23 25 27 29 31 33 35
1751 37 38 41 43 45 47 49 51 53 55 57 59

This in effect means that there's a leap month every 32nd or 33rd month, alternately. It should be easy to calculate by hand.

In the calculation of the calendar you count years and months from the epoch which is at the beginning of the third month in 1747. The number of months from the epoch to the year in question is (((number-1747)*12*67+10)/65+17/65). We count 12 months, for each year, but since there are 67 lunar months to 65 years, we multiply it with 67/65. There are 10/65 left over from previous months. Phugpa rounds the fractions in this case from 48 up, so we add 17/65 to get the correct number of months. The table above represents the remainder in 65ths, when 17/65 has not been added.

If you know the number of months from epoch (m), you can calculate the year and month:

  g=(m+2)*65/67+40/65 'number of solar months
  i=floor(g/12) 'current solar year from epoch
  j=floor(g)-i*12+1 'current lunar month
  k=i+epoch 'Gregorian year of Цагаан сар

This formula is not used in Tibetan calculations. In Phugpa you should use m+1 for m+2 and 62/ 65 for 40/65.


To find the date we have to calculae where the sun and the moon are. The dates in a Tibetan calendar are numbered so that a day is 1/30 of the orbit of the moon with full moon occurring on the 15th. Account is taken of the variable speed of the moon. This means that there may be dates missing or two days may have the same number. Mongolia also has followers of the Yellow system, which numbers days consecutively. As far as I have been able to ascertain, it is the Chinese calendar imposed by Manchus on the Mongolians.

To calculate the date, one starts with the mean weekday, then the mean sun. Then one corrects these with solar and lunar equations to get the true date and the true sun.

    m0=2015501+343736+14056200/15271200 'True day päivää myöhempi

mean_date= n*m1+d*m2+m0
    s0= 38588382/39074400 'tarkistettava  407193840/412322400
mean_sun (n*s1+d*s2+s0)-floor(n*s1+d*s2+s0)

    a0=3046/3528 'Henningillä 0
    a2=3781/105840 'Henning
    'a2=1/28 'Phugpa
anomaly_moon(d,n)=return (n*a1+d*a2+a0) -floor(n*a1+d*a2+a0)
The orbit of the moon is divided in 28 points. Moon_tab refers to a function which takes the values from the following table. For the first quarter of the orbit the value of  moon_equ grows from 0 to 25 and then goes down again to reach zero when 28*anomaly_moon is 14. Then  moon_equ becomes negative and descends to -25 when 28*anomaly_moon is 21. For the last quarter moon_equ grows again to 0. If 28*anomaly_moon is an integer, the values can be directly looked up in the table. For the values between integers you multiply the difference between the two consecutive integers and multiply it with the decimal part of 28*anomaly_moon.

For instance

0 0 5
1 5 5
2 10 5
3 15 4
4 19 3
5 22 2
6 24 1
7 25 1

    epoch =1747




  if i>7  and i<14 then
    return moon_tab(14-i)
  elseif i>14 Then
    return -1*moon_tab(i-14)
  elseif i>21 Then
    return -1*moon_tab(28-i)

The Chinese New Year is earlier than the Mongolian. The earliest date for the Chinese New Year since 1900 is 21st January, while the earliest date for Цагаан сар is 28th January. It is a week's difference.

The Mongolian reform was published in 1747 (the first year of cycle XIII). The epoch according to Henning is Sunday 9th April 1747, Julian day: 2359237. However, Berzin says the new calendar was started in 1786 and the starting point of the calculations is the 40th year of the 60 year cycle, which presumably is cycle XIII, that is 1786.

The length of the month in the Tibetan calendar, 167025/5656 days, is quite near the correct value. With this length of the month the Mongolian solar year in the 76-year cycle is 365.2467338 days, which means about four and a half days too long in a millennium when compared with the tropical year (365.24219 days). Better values could be reached by 123 leap years in 334 years (12 123/334 months ≈ 365.2420804 days (about one day too short in 10000 years), 12 253/687 months ≈ 365.2422091 days, or 12 882/2395 months ≈ 365.2421911 days. Of these 123/334 was used by the formula for Chinese leap years in the Islamic calendar mentioned above.

Janson the calendar is gets later 3 days in a century.

Links and references

Dershowitz, Nachum&Edward M. Reingold 2008. Calendrical Calculations. Cambridge University Press.

Henning, Edward  2006. Kālacakra and the Tibetan Calendar. Columbia University Press.

黄明信 2007. 黄明信藏学文集:藏历研究. 中国藏学出版社.

Janson, Svante :  Tibetan Calendar Mathematics

Qizheng tuibu 1985 [facsimile edition of a Ming dynasty book] 七 政推步

mongγolčud-un odun orun jiruqai-yin uqaγan-u teüke ("Монголчуудын одон орон зурхайн ухааны түүх")
ISBN 9787807225331
A history of  the astronomy and calendar of the Mongols. In Uyghur script Mongolian. From what I gather there is nothing on the reformed Mongolian calendar.

Монгольско–русский словарь/Монгол орос толь, Москва 1957. The information on years and cycles (pp. 712–715) is in tables with the elements in columns and animals in rows. The cycles are listed.

鍾易遠 (Zhōng Yìyuǎn) 1995. 新編萬年曆 (Xīn Biān Wànniánlì). 跨世紀 (Kuàshìjì)

Л.Тэрбиш: Монгол зурхайн цаглабарын уламжлал хийгээд өнөөгийн байдлын талаар уншигч танаа учирлах нь
The main source because it has numerical information. A long description of the development. Terbish is widely mentioned on Mongolian pages about the calendar.
The people mentioned:
Гармаваа Ранжүндорж (rang 'byung rdo rje)  /rtsis gun btus pa/
Цүрпүваа (mtshur phu ba )  Жамьяандондов-одсэр
Пүгваа (phug ba) Лхүндэвжамц
Дэсрид Санжаажамц (sde srid sangs rgyas rgya mtsho) /rtsis gzhung be dur dkar po/
Сүмбэ ханбо Ишбалжир /rtsis gzhung dge ldan rtsis gsar)/
“Цагаан биндэръяа” хийгээд Лувсанданзанжанцан(1639-1704) (1789)
 Дэчингалавын сүмийг байгуулан “Цагийн Хүрдэний Язгуур үндэс” (1806)
A newer version?
Монголын одон зурхайн тоолол ба “Баясгалан” хэмээх усан луу жилийн өнгө, нуруу

A calendar for the iPhone:

Terbish is also the author of a Kalmyk astrological calendar.

Alexander Berzin, Tibetan Astro Science: 2 History and the TibetanCalendar. 1986.

Dieter Schuh: Tibet-Encyclopaedia
Excellent descriptions of Tibetan astronomy and calendar, among other things: A set of dates for New Years. It is not clear if these are from the official list of dates calculated by the Gandantegchinlen Monastery. I haven't been able to find the official list, “Жаран жарны цаг тооны бичиг” (1207-гоос 4626 он дуусталх 3600 жил). The article mentions the book Л. Тэрбиш: Монгол зурхайн цаг тооны бичиг. (1991)билгийн-тооллын-цагаан-сарын-лавлах?quicktabs_1=1Сагаалган Another set of dates for the day before New Year (битүүн), different from the above (for Buryat New Year?). There is a link to this page from the English Wikipedia page. [Link dead 11.8.2011. Merged with the following]Цаган_Сар New Year dates [Accessed 11.8.2011]

If you change the date and refresh it (Перейти), and then click on the left for the commentary (Показать все комментарии), you can scroll down in the window and check the Лунный день. You have to know the ordinal numbers in Russian. In 2008 New Year's day was one day earlier than in the Mongolian list, so this calendar is not of much help.

The site of the Buddhist monastery in St. Petersburg. They have published a Buddhist calendar based on the chief astrologist Содбо Айсуев from Ivolga in Buryatia. A list of New Years for 112 years from 1896 to 2006. This page seems to be written by Terbish, so this may be the official list. The first 2003 is a typo and should be deleted. An important reference.

Билгийн тооллын цагаан сарын лавлах 1924-2012билгийн-тооллын-цагаан-сарын-лавлах?quicktabs_1=1
A list of New Years. Looks reliable.

A daily horoscope with a monthly calendar: Mentions the difference of one month between the Chinese and Mongolian New Years in 2001 Contoversy over the year 2009

Mongolischer Kalender [Link dead 11.2.2012]
Examples of dates missing or two days with the same number in the year 1997/1998. Looks reliable but information on the last two months of the year (a leap year) is missing.
Online Mongol calendar, only for a couple of months, but changing the URL you can find more. Lots of mistakes, missing lunar day numbers, missing months, dates in descending order. An important reference if the rest is correct. Lunar months are not indicated. [Links dead 11.8.2011] I have checked the dates of the calendars I printed out from this site. There is not one discrepancy between them and the New Genden Calculations for the period from March, 2004 to December 2007. Here's a sample day from these calendars:

2004 оны 03 сарын цаг тооны бичиг
Аргын тоолол Билгийн тоолол Жил өдөр Однууд Мэнгэ Хөлөл Барилдлга Шүтэн барилдлага Нар ургах, шингэх
шарагчин туулай 4, 23
1 цагаан Огторгуй Рашаан Төрөxүй 07:35-18:25

Аргын тоолол: Gregorian date and day of week.
Билгийн тоолол: Lunar date and day of week in alternative Sanskrit names for the planets.
Жил өдөр: the day of the year in cycles of 60. These are the same as in the Chinese calendar.
Однууд: ‘stars’, the longitude of the moon at the beginning of the calendar day, longitude of the true sun, the longitude of the moon at the end of the lunar day, expressed in full lunar mansions (27ths of the ecliptic).
Мэнгэ: the nine numbers and their associated colours.
Хөлөл: the trigrammes.
Барилдлга: the yogas (Henning 2007:204). These seem to be a function of the elemtn of the weekday and the longitude of the moon at the end of the lunar day.
Шүтэн барилдлага: the links (Henning 2007:205), the Twelve Nidānas, arranged according to the phases of the moon.
Нар ургах, шингэх: sunrise, sunset.

Jacqueline Hobbs: Sumpa Khenpo in Amdo The dates for the current year of the historical calendars agree with the official calendar from Dharamsala. [Accessed 11.2.2012]
New Year dates from 1900 to 2009 compared to the Chinese dates. Same as in Wikipedia but the dates differ from the Buryat list, although the same new moon is meant. Neatly arranged in 19-year cycles. From 1959 onward a different pattern of
Terbish about missing days. Alas, in Mongolian. Terbish in English about missing days. Controversy over the date of the New Year: the Mongolian calendar places the New Year on ‘black wind days’, which is bad. [Link dead 29.12.2009] Controversy over the date of the New Year: the Mongolian calendar avoids the New Year on ‘black wind days’, which would be bad. Controversy about the date of the New Year. Some think the precise and scientific Chinese calendar should be used instead of the tradition Tibetan calendar. Terbish thinks it would be disrespectful of Mongolian science and traditions. In Chinese.

A video clip in Mongolian of a discussion about the date of the New Year in 2012. The Chinese date is 23rd January, a day later than the Mongolian date. [Accessed 11.2.2012] Opposes Tibetan dark customs and Terbish's calculations. [Accessed 15.8.2011] Presumably about the history of the calendar. [Accessed 15.8.2011] Two versions of the Mongolian lunar calendar generally exist in the country. One is the Yellow calendar, influenced by the Chinese lunar calendar, and the other is the Tugsbuyant calendar, closely related to the Tibetan lunar calendar. In 1911 the Tugsbuyant calendar was officially recognized by the Bogd Khan. In English. [Accessed 15.8.2011]

Many Mongolian websites have a daily horoscope. The information follows the same format and it is not obvious how ыou can move from day to day. Official Tibetan calendar from Dharamsala List of the years of each sixty-year cycle and months in one year. In Chinese. Astrology Ishbaljir was an Oirat

Each has an associated mantra (тарни).
Buddhist terminology
Twelve links of Dependent origination – шүтэн барилдахуйн 12 гишүүн
Primordial ignorance – мунхаг
Conditioned or formative actions – хуран үйлдэх, үйл
Consciousness – тийн мэдрэхүй, хуран мэдэл , сэтгэл, ухамсар (тийн мэдлийн үе гишүүн орчлонд тусах)
Name and form – нэр болон дүрс
The five sense bases and the mind – төрөн түгэхүй
Contact and its desire for the object – мэдрэхүй, хүрэлцэхүй
Sensation or desire giving rise to feelings of pleasure and pain – амсуурга, сэрэхүй
Craving – шунах
Grasping – авахуй
Potential existence – оршихуй, сансар
Birth leading to endless rebirth – төрөхүй
Aging and death leading to endless cycles of life and death – өтлөх ба үхэх
Every day has one of these. The succession starts, following the Tshurpu tradition, on the first day of a lunar month (Henning 2007:206). The names go down the list for a full cycle of twelve, then goes back 10 steps. The 16th lunar day is indicated by the link that started the descent. Then the direction is reversed until the end of the lunar month is reached. The first lunar month is associated with хуран үйлдэх, the second with тийн мэдрэхүй, and so on.

The 12 nidānas, which are usually given among the daily information in a calendar.
12 шүтэн барилдлага
танин мэдэхүй /vijnana/ туулай
нэр дүрс
түгэхүй /salayatana/ могой
хүрэлцэхүй /phassa/ морь
сэрэхүй /vedana/ хонь
хурьцахуй /thanha/ бич
авахуй /upadana/ тахиа
төрөхүй /jati/ гахай
өтлөх үхэхүй /jaramarana/ хулгана

Bagua (Суудал, хөхөл)
хий ☴ гал ☲ шороо ☷
мод ☳
төмөр ☱
уул ☶ ус ☵ огторгуй ☰
These are assigned to every day in clockwise order.
Yearly properties units for measuring time
Measures of time
1 хоног (24 hours) = 60 мөч
1 мөч = 60 чинлүүр
1 чинлүүр = 6 амьсгал
1 амьсгал = 67 агшин
1 агшин = 707 дэнс

Double hours (doubtful information):
Монгол тооллийн цаг
1. Хулгана- 23.40-1.40
2. Yхэр- 1.40-3.40
3. Бар- 3.40-5.40
4. Туулай- 5.40-7.40
5. Луу- 7.40-9.40
6. Могой цаг- 9.40-11.40
7. Морь- 11.40-13.40
8. Хонь- 13.40-15.40
9. Бич- 15.40-17.40
10. Тахиа- 17.40-19.40
11. Нохой- 19.40-21.40
12. Гахай- 21.40-23.40

Хонь    Yхэр     Ихэр     Мэлхий
Арслан     Охин     Жинлүүр     Хилэнц
Нум     Матар     Хумх     Загас

Alternative names for the days of the week, used for lunar dates:
Нар (Адьяа), Сар (Сумьяа), Ангараг, Буд, Бархасвадь, Сугар, Санчир

Phases of the moon
битүү сар new moon
шинэдийн сар waxing
тэргэл сар full moon
хожидын сар waning moon
In Russian. The Mongolian calendar was made official in 1911 instead of the Chinese yellow calendar. During the years of repression the Mongolian New Year was celebrated as a feast of livestock breeders. A short biography of Sümbe hamba Ishbaljir, including the full name of his astronomical work. Another name of the work.
His collected works are available at Uppsala University Library. Kalmyk kalendar. Nothing on the mathematics. The New Year was earlier in the autumn. In Russian.
A rather detailed biography of Sum-pa mkhan-po [Accessed 11.8.2011] German Wikipedia article [Accessed 11.8.2011] An illustrated article on Sum-pa mkhan-po, in Chinese. There are several Chinese forms of his name.
松巴堪布伊希巴勒珠尔 Officially Tibetan calculations are still done on a sand board. Interview of an astrologer.
Calendar history from the National Archives


February 2012 March 2012
Ня Да Мя Лх Пү Ба Бя Ня Да Мя Лх Пү Ба Бя

19 210 311 412

18 29 310
513 614 715 816 917 1018 1119 411 512 613 714 815 916 1017
1220 1321 1422 1523 1624 1725 1827 1118 1219 1321 1422 1523 1624 1725
1928 2029 2130 221 232 243 254 1826 1927 2028 2129 2230 231 242
264 275 286 297

253 264 275 286 297 308 318