A Note on the Indian(Hindu) Calendar System

In a previous post, I’d mentioned how the names of months in the traditional Indian calendar were derived from the names of stars and how these names had also traveled to China. Some of my readers asked me to write a bit more about the Hindu calendar system, and provide answers to frequently asked questions such as why most Hindu festivals such as Yugadi or Deepavali do not occur on the same date every year, in a simple language. The purpose of this post is to do exactly that.

To give some background before diving into the specific intricacies of the Hindu calendar system- the Hindu calendar, or the Panchanga, keeps track of the year, and various festivals that are celebrated through the year. The name Panchanga comes from the five primary elements, known as angas, that make up the calendar — Tithi, Vara, Nakshatra, Yoga and Karana. I won’t get into the details of how various angas of the Panchanga are calculated in this article but suffice to know that most of our festivals are determined by tithi or nakshatra, and masa (month).

Early mankind was very much influenced by celestial events and had noted the cyclic nature of the movements seen in the night sky. While this has happened in all civilizations around the world, in India we can be very certain that it had reached a fairly advanced state of calculative and predictive measurement of time, at least around 3500 years before present times. The Vedanga Jyotisha of Maharshi Lagadha, which can be dated to around this time (There are some different opinions about the date- with estimates going to as back as 3800 years before present, to as low as 3100 years before present), describes a calendar system with a year of 366 days long, with 12 months of 30 days nominal length per year, and with intercalation (adding of additional month) to bring the seasons not to drift and the year made of 12 months is brought back in synchronization with the 366 day long year at the end of a Yuga — a period of 5 years, as defined in the Vedanga Jyotisha. It can be noted that there is another interpretation that the yuga in the Vedanga Jyotisha was 19 years long, but that does not make much difference for the purpose of this article.This yuga referred to in the Vedanga Jyotisha has no relation to the yugas that go by the names Krta, Treta, Dvapara and Kali. Those are of much larger periods of time and those concepts arose later than the text of Vedanga Jyotisha.

It is clear from the text of Vedanga Jyotisha that both the movement of the moon, and the movement of the sun, as seen with the background of stars, was quite well understood in India by its time. The northerly and southerly movement of the sun in the sky and its relation to the seasons on earth were also understood. Suffice to say that the calendar described by Vedanga Jyotisha took care of the needs for a civilization by providing a calendar for their agriculture, ritualistic and other life needs.

Panchanga calculations used today for determining festivals and other rituals are datable to more than 1500 years and are advanced than what Vedanga Jyotisha describes. But we can understand the basic principles without getting into details. Two methods of measuring the year, namely the sauramana and chandramana years are in use in India apart from the common year starting in January. Sauramana -‘sun measure’, or the solar year is a way of reckoning time using the movement of the sun. Chandramana-‘moon measure’ is a way of keeping track of the year with the moon’s movement. Although commonly it is called a ‘lunar’ year, it is apt to call it luni-solar year, because it is not just the moon’s movements that determine this year, as we will see soon.

The solar year is the time it takes for the sun to return to the same relative position with a star in the sky, as seen by an observer on the earth. One may ask how to find out which star the sun is appearing close to, when the stars are not seen in daylight. Observations made before the sunrise, and after the sunset help to determine the actual position of the sun. It was thus understood several millennia ago that the sun took somewhere between 365 and 366 days to reach the same point in the sky. This is exactly the time taken by the earth to complete one revolution around the sun, and by far it is quite an accurate indication of seasons too, for a given place. This is what is traditionally called the solar year. The anchor for the beginning of the year would be set to some well known star. At the time of Vedanga Jyotisha, a yuga (and the new year as well) began when th sun and moon were near the star named Shravishta (or Dhanishta). Today, the solar year is pegged to a star named Ashwini.

Then you may ask, if it were so perfect why doesn’t the sauramana year be the only one in use? Just think of the convenience, or the lack of it. Since stars are not visible during daytime, the position of the sun must be estimated by watching the stars that are leading the sun in the dawn, just before sunrise and following the sun during dusk, just after sunset. It would be quite convenient to have an alternate mechanism where seasons and years can be measured by direct observations of. Here is where the moon in our night sky, along with stars, becomes a convenient tool. The daily movement of the moon across the sky is perceptibly large, and can be easily tracked.

It was long discovered in India (and other civilizations of the world ) that the moon takes between 27 and 28 days to come back to the same position in the sky with reference to a given star. Since the moon shows different phases of illumination, it was seen that the full moon in the sky repeated at an interval between 29 and 30 days. This is how a month of 30 days length came into vogue. Out of the 30 days of the month, the moon goes from new moon to full moon in 15 lunar days or ‘tithis’. In each tithi, the moon travels the same distance in the sky and the tithi does not have to have any alignment with the practical day, starting at sunrise. The duration of the tithi does not have to be 24 hours, but less or more depending where the moon is in its orbit around the earth. Given the fact 12 full moons occurred in a span of a solar year of 365/6 days, the year was set to have 12 months. With these coordinates of the masa (month) and tithi (lunar day), any specific day within a year can be identified.

Since the moon took 27/28 days to go around the sky, the sky was divided into 27/28 equal parts. A star or a group of stars ( called a nakshatra) within each division was assigned as the representative star (Yogatara). These nakshatra divisions are seen in the Veda itself, and date to the very beginnings of Indian civilization. There are some efforts to find the antiquity of the Veda by analyzing the nakshatras as listed in there, but that discussion is outside the scope for this article.

Although initially a 28 star-cycle was in use, one star (Abhijit) was dropped at some point in time, and we are left with the 27 stars (Ashwini to Revati, as counted today). The time in which the moon crosses the boundaries assigned to a yogatara is identified by the name of that nakshatra. So on a specific day if the moon is at Ashwini, the following day it will be at Bharani. Since the moon’s orbit is not a circle, the time taken is not constant and the moon may spend slightly different times at each of the nakshatras. Since the moon can cross a star-boundary at any arbitrary time of a day, the nakshatra for a given day can change at any time of the day, but for practical purposes, the tithi and the nakshatra for a day are determined by what they are at sunrise .

It was also observed that the full moons tend to occur near certain stars — and hence the months were named after those stars. I have written in detail about this in the post titled The Festival of Kama. With these 27 stars named and their boundaries determined, it was also applied to the position of the sun on its movement along the sky. Since there are 12 months in a year, the sky was also divided into 12 equal parts with 2.25 nakshatra divisions (2.25x12=27) corresponding to the distance covered by the sun in one month, since the sun covers the entire 27 nakshatra divisions in exactly one year. These 2.25 nakshatra divisions correspond to one rashi or the constellations of the Zodiac. There are some conflicting opinions on whether the rashi concept came as an import or indigenous — but the source does not matter, as long as we know the sun covers one rashi in each month. These are the solar months, and the day the sun moves from one rashi to another is called a Sankramana (or Sankranti). Thus there are 12 sankramanas in a year. Makara Sankramana, occurring around January 14th and Mesha Sankramana occurring around April 14th of each year, are widely celebrated festivals. It is the Mesha Sankramana, or Vishu, that is considered the beginning of the solar ‘sauramana’ year. Since the revolution of the earth around the sun is of a fixed duration, it must also be clear why the festivals such as Makara Sankranti or Vishu occur at the same calendar dates.

By now you’d also have understood that the year based on 12 lunar months falls short by about 11 days (29.5x12=354 days versus the 365 days required for the solar year), each year. If we allow this to accumulate, what would happen? Any festival you are celebrating, would fall out of season. For example, Yugadi that is supposed to occur in the months of spring, will very quickly fall into winter and then into the autumn and so on. To avoid this situation, approximately once in about 3 years (generally at 33 month intervals), an additional lunar month is added thus bringing the lunar and solar years almost in sync. This is called ‘adhika-masa’ or the extra month. By doing this the constant drifting away of festivals is avoided. This is also the reason why I said earlier that the term luni-solar describes the term chandramana more accurately than lunar.

To see this playout in effect: In 2021, Chandramana Yugadi was celebrated on April 13th. In 2022, on April 2nd. In 2023 it will be on March 22. Before 2024, there will be an occurrence of adhika masa (extra/intercalary month) and instead of falling back to March 11th, the festival would fall on April 9th. When exactly the adhika-masa is inserted is based on the sankramanas occurring in a lunar month. A lunar month that has no sankramana would be termed as adhika. So in such cases, you will have the same month named twice. For example, you might have an adhika-ashadha (excess-ashadha month followed by nija-ashadha (true-ashadha) month, when there is no solar sankramana in a month that was supposed to be Ashadha. With the process of these additional months, the chandramana year synchronizes seasons with the chandramana months.

Now you can see when we celebrate birthdays, or other festivals based on the Indian star calendar, we are actually doing it when the orientation of the moon with respect to stars is very close to how it would have been at the time of the original event it commemorates, because of their relation with the tithi and/or nakshatra of the day. Now we can see there is nothing ‘unscientific’ about Indian festivals occurring on different dates each year. It is just a different frame of reference.

So far you noted all these measurements of time in the Indian calendar are based on the movement of the brightest bodies seen in the sky, i.e. the sun and the moon. However there are calculations that involve the movement of planets like Jupiter (Guru) and Saturn (Shani). Jupiter takes about 12 years to go around the sun (and thus takes a similar amount of time to go back to the same star in the sky on its path). Saturn does the same thing in about 30 years of time. By the time Saturn covers the sky twice, Jupiter covers it five times and at the end of 60 years, both Jupiter and Saturn would repeat their relative positions with reference to a given star. This is the basis of the 60-year samvatsara cycle that is followed by the Hindu calendar.

While this article does not provide exhaustive explanation or details of the depth of calculations that go into making the Panchanga, it should provide to the interested reader some basic information and clear up common misconceptions.

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(P.S: All Samskrta words are italicized but no diacritics are provided because these are quite commonly used words)