Kālacakra Calendar

The Kālacakra Calendar

A key component of the Kālacakra system is the calendar described in the first chapter of the Kālacakra Tantra. Here are published several versions of the calendar, calculated for different major world cities; there is also an archive (covering 600 years) of traditional Tibetan calendars and open source software to calculate both Kālacakra and Tibetan calendars.

Below, there follows an introduction to the calendar.

Kālacakra calendar:

  Calendar description – a general description of the Kālacakra calendar.
  Published calendar explanationUPDATED: a description of the Kālacakra calendar using modern astronomy published here.
  Symbolic details – some details about the information in the calendar.
  Choose calendar – click here to view the list of calendars available.
  Kālacakrāvatāra. – Sanskrit edition of the Kālacakrāvatāra of Abhayākaragupta.
  Astrology associated with Kālacakra – notes on the astrology associated with the Kālacakra calendar.
  Download open source calendar softwareUPDATED: software to create the Kālacakra calendar (modern astronomical calculations).
  Open source Kālacakra karaṇa calendar – calendar software created for teaching and research purposes (traditional calculations).
  Example Kālacakra karaṇa calculations – a worked example of calculations for one day of the karaṇa calendar from the Kālacakra Tantra.
  Early epochs – early examples of epoch data for the Kālacakra calendar.

Tibetan and Bhutanese calendars:

  Traditional Tibetan calendar archive – an archive of traditional Tibetan calendars.
  Open source Tibetan calendar softwareUPDATED: software for traditional Tibetan calendars, siddhānta calculation systems.
  Open source Tsurphu calendar software – open source software for Tshurphu tradition of Tibetan calendar.
  Error correction system – a description of the calendar system of Zhonnu Pal.
  A reformed Tibetan calendar – details of a recent attempt to reform the Tibetan calendar.
  Open source Sherab Ling calendar softwareUPDATED: software for the Tibetan calendar published by Sherab Ling monastery.
  On intercalary months – intercalary months in the Kālacakra and Tibetan calendars.
  Epoch data – epoch data used in the Kālacakra calendar and a variety of Tibetan calendars.
  Bhutan calendar problem – discussion of a unique problem in the Bhutanese calendar.
  Open source Bhutanese calendar software and calendar archive – software for the Bhutan calendar together with calendar archive.


One of the main topics to be discussed in the first chapter of the Kālacakra Tantra is the creation of a calendar. There are many misconceptions regarding this system. The Tibetans used it as the basis for their calendar, which theoretically started in 1027, but have mostly never followed the precise instructions as given in the original Kālacakra literature; as a result, the Tibetan calendar contains significant errors. There are therefore strong reasons for saying that the Tibetan calendar is in need of reform. (See Svante Janson for a description of the Tibetan calendar in modern mathematical notation; also see this page for software and source code to calculate traditional Tibetan calendars.)

So, the main Kālacakra calendar presented here is not a Tibetan calendar as can be purchased nowadays in Lhasa or Kathmandu, but is based as closely as possible on the instructions given in the Kālacakra literature, with the exception, of course, that we need not use all of their methods, and can instead use modern technology and astronomical calculations where appropriate.

However, there is one calendar that was developed in Tibet in the 15th century in the system known as the "Correction of Error" ('khrul sel) that closely followed the instructions in the original Kālacakra literature. If that calendar had been developed further and then maintained by means of regular adjustment on the basis of observation, it would be essentially the same as the calendar presented here (it would also, of course, also include Tibetan/Chinese symbolic information).

Another misconception – very common in the west – is that the Tibetan, and therefore the Kālacakra, calendar is based on a sidereal, rather than a tropical zodiac. Exactly the reverse is the case.

Ayanāṃśa. Some Indian systems describe the difference between the beginning of the sidereal and tropical zodiacs by this term, ayanāṃśa. As the First Point of Aries of the tropical zodiac is moving slowly backwards through the sidereal zodiacal constellations (the process known as precession), its value (currently around 22°-24°) is constantly increasing. One sometimes reads that the Tibetan system uses an ayanāṃśa, and even that Tibetan almanacs print its value (Tibetan Astrology, Cornu, p.129). But such statements are pure fiction – the concept does not exist in the Tibetan system, and Tibetan calendars publish no such information or anything that could be misinterpreted as such.

It is certainly the case that the First Point of Aries in the Tibetan way of measuring longitude is offset from that in a proper tropical zodiac, but this is due to the belief that the solstice is observed earlier in Tibet than in India. This offset (1;43,30 in the Phugpa tradition) does not slowly increase with time – other than as a result of errors in the calculation – and has remained fixed for nearly 600 years. The fact that this seasonal offset has a value similar to the current ayanāṃśa is simply coincidence. The offset was fixed at a time when the ayanāṃśa was about 23 its present value.
The difference between these two zodiacs is as follows. In both cases, the zodiac is a division of the ecliptic into twelve equal parts called signs, or zodiac signs. These are therefore all 30° in size. The ecliptic is the path the Sun follows through the sky during the year, and the position of the Sun, and also of the Moon or planets, at any one time is given as a measure of angular distance from a starting point in the ecliptic. This distance is called longitude.

The zodiac begins with the sign of Aries, and the point right at the beginning of Aries is called the First Point of Aries. In the west, longitude is measured in terms of degrees, or of a combination of signs and degrees. So, if the Sun is said to be at a point 10° within the sign of Gemini, as Gemini is the third zodiac sign, the Sun is therefore 70° from the First Point of Aries.

The difference between the two types of zodiac lies in the definition of the position of the First Point of Aries. In the tropical zodiac, the First Point of Aries is defined as the position of the Sun at the vernal equinox – at this point the plane of the Earth's equator and the ecliptic cross, and when the Sun is in that position in the Spring, day and night are of equal length. The tropical zodiac is the one most commonly in use.

Due to the phenomenon known as the precession of the equinoxes, the tropical First Point of Aries is slowly moving against the background of the stars – the movement is at a rate of approximately 50 seconds of arc each year.

In a sidereal zodiac, the First Point of Aries does not move relative to the stars, but is a point within the fixed stars. It's position varies with different traditions, but it is in the region bordering the constellations of Pisces and Aries. The uncertainty regarding the definition of the sidereal First Point of Aries is not the only problem with a sidereal zodiac. Due to precession, the ecliptic moves relative to the stars, and the point of the vernal equinox on the ecliptic moves away from this point in the stars. So, if the sidereal First Point of Aries is defined for some hundreds of years ago, the Sun no longer actually crosses that same point at the time of the equinox, and as the years pass, moves further away each time it passes.

Approximately 1,500 years ago, these two zodiacs coincided, but due to the precession of the equinoxes, the tropical First Point of Aries is slowly moving against the fixed stars, and has by now drifted to a point approximately on the border between the constellations of Aquarius and Pisces.

New Year in the Kālacakra calendar takes place in spring, and as the system is based on a tropical zodiac, it will always occur in spring. However, if the calendar were instead based on a sidereal zodiac, New Year would slowly drift later through the seasons.

It is surprising that so many westerners believe the Kālacakra and Tibetan calendars to be based on a sidereal zodiac, because the Kālacakra Tantra commentary, the Vimalaprabhā, leaves no room for any such view, and makes the point very strongly.

Most Indian systems of astrology and calendars are in fact based on sidereal zodiacs, and the Vimalaprabhā explicitly criticises such systems for not understanding the true position of the Sun. It describes how the calendar needs to be adjusted regularly by means of direct observation in order to correct the solar position.

It states that without a correct value for the longitude of the Sun, then the longitude of the moon will be wrong, and so will those of the other planets. With all these wrong, any prognostications made will also be wrong. It states that such methods are meaningless.

Tibetan gnomon
Text book drawing of a Tibetan gnomon
The observation that it says is needed is to time the occurrence of the winter solstice, by means of determining with a gnomon (thur shing) the longest midday shadow of the Sun. Once that has been determined, then the Sun's longitude has to be corrected for that time to equal 0° Capricorn. 0° Capricorn is the exact position of the Sun at winter solstice in a tropical zodiac, and the Vimalaprabhā calls this the primary definition (rtsa ba'i nges pa, mūladhruvaka) for it's calendar. The point could hardly be made more clearly.

(The Vimalaprabhā actually gives the corrected longitude as 20;15,0, which is a measurement in a system that divides the zodiac into 27 equal bands, each of which are further subdivided into 60 parts. A simple calculation will show that this equals 0° Capricorn.)

The methods used by most Indian systems rely on complex calculation systems that were described in textbooks (siddhānta), and expected to be accurate over long periods of time. Clearly, the Kālacakra system is opposed to this method, because over long periods of time small errors will accumulate and become significant. The methods described by the Kālacakra system would have seemed quite radical in 10th century India, and looked at in this way, the Kālacakra system has quite a reforming spirit to it.

Perhaps these issues were not well understood in Tibet. As most Tibetans have not adjusted their calendars according to the methods described in the Kālacakra literature, their main calendar now uses a position of the Sun which differs from that in a tropical zodiac by about 36° – more than a whole sign of the zodiac. Their solar position is also not consistent with a sidereal zodiac, and is simply wrong – it is not a matter of sidereal or tropical. The intention was to base it on the Kālacakra system and its tropical zodiac, but the methods needed were either not understood or were for some reason rejected.

The irony of course is that the Tibetans, who have otherwise preserved the Kālacakra system so well, when deriving their calendars have fallen victim to just those errors that the Kālacakra so strongly criticises.

    E. Henning.
    Last updated 27 July 2013.
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