Overview

When a calendar reform was brought under way in India in the 1950s, 30 calendars of over-regional significance were counted on the subcontinent. This diversity made it hard to implement any reform, and the National Calendar eventually proposed did not make it into civil or religious life. Besides the calendars described in this article, the Islamic calendar is used by Muslims in India.

The basic elements of Indian calendars - with the exception of the Islamic calendar - are similar but subject to various variations. The calendars are based on computations simulating the apparent movement of sun and moon. With different assumptions for the length of months and years in use there are many differing variations of calendars. Furthermore, there are many regionally different months names and beginnings of the year and many eras in use. Thus this article must be understood as giving a basic structure of Indian calendars without describing a certain calendar actually used.

Time Units

Unlike most of the other calendars Indian calendars do not employ the solar year and day (i. e. tropical year and solar day) but the resprective sidereal units. Thus, the calendrical year is based on the sidereal year defined as the time between two sucessive passes of the sun through a certain star's circle of declination. Lunar days and sidereal months are also used, and in certain lunisolar calendars lunar year and lunar month are taken into account, too.

Year Length

Astronomical knowledge of Ancient India was written down in scientific treatises, called siddhântas. In them, values for the lengths of months and years were given representing the latest knowledge at the time the siddhânta was written. The values range from 365.258681 days in the Âryabhatiya(1) to 365.258756 days in the Sûrya-siddhânta(2) and are all too long compared with the modern sidereal year length of 365.25636 days. Nevertheless they are still in use for Indian calendars today.

The beginning of the year is slowly moving with respect to the actual weather conditions. Although this was known in Ancient India already there have never been attempts to introduce the tropical year as the basic unit for the calendar.

Month Length

Most lunisolar calendars including the Jewish calendar and the lunar calendar employed for the determination of Easter, use the lunar month as the basic time unit. In different Indian lunisolar calendars the lunar month is used, mixed with the sidereal month. The latter is about two day shorter than the former with different values given in the siddhântas.

Tithi

Unique is the definition of a lunar day having a mean length of about 22.5 seconds shorter than that of the solar day.

In the course of a synodic month the angle between sun and moon is growing from 0° at new moon to 180° at full moon and finally to 360° at the next full moon, the angle measured in the same direction during the whole month. This full circle of 360° is divided into 30 equal divisions of 12° each. The time it takes the angle between sun and moon to increase 12° is defined as a lunar day or tithi. The 30 divisions having the same size, a tithi has a mean length of ¹/₃₀ of a synodic month or about 23 hours 37 minutes and 28 seconds. However the actual length of the tithis as well as the solar days vary due to the irregularities in the movements of sun and moon.

Paksha

Every lunar month consists of two halves of 15 tithis each. The "bright" half (shuklapaksha) starts with the new moon, the "dark" half (krishnapaksha) with full moon.

With these time units a calendar system was developed which at a first glance seems to be quite intricate. However the basic rules are quite simple and clear. Because of the innumerable variations, different lengths of months, years, beginnings of the year and month, and names of months it is not possible to derive reliable calculation algorithms.

Ritu

Finally, the year consists of six seasons, called ritu, of two months each.

Star Constellations

Nakshâtras

For lunisolar calendars, the ecliptic was dividied into 27 nakshâtras (Lunar Houses) characterized by certain constellations. The number 27 was choses so as to correspond roughly to the number of days in a sidereal month, making the moon pass a nakshâtra each day approximately. Sequence and names of the nakshâtras and the stars the constellations are formed of are shown in the following table.

These constellations were in use at the beginning of the first millenium BC already, it seems. Later, astronomers inserted a 28th nakshâtra between Uttarashadha and Shravana called Abhijit and consisting of the stars α, ε, and ζ Lyrae.

Zodiacal Signs and Sankrântis

Twelve zodiacal signs play a certain role in solar calendars and had their origin in the classical world of the eastern Mediterranean. Such a sankrânti got names in Sanskrit, the classical language of ancient India, but never could replace the nakshâtras. The Sanskrit names and the corresponding zodiacal signs are shown in the following table.

The sun's entry into one of these signs is also called sankrânti, e. g. Mesha-sankrânti for the entry into the first one. The astronomical beginning of the year coincides with the Mesha-sankrânti. The first day that begins after the Mesha-sankrânti is taken to be the first of the new new, however, there are regionally different reckonings here, too. Since the sections of the ecliptic are of equal size (i. e. 30°) and the sun's apparent velocity is not constant, month lengths vary from 29 days up to 32 days. The time the sun needs to pass through such a section ranges from 29.4 days to 31.6 days.

Lunisolar Calendars

A year of these calendars consists of twelve or thirteen months strictly bound to the moon's phases. A special feature of Indian calendars is that, besides of the insertion of a leap month, sometimes a month is omitted; even single days are intercalated or extracalated. The rules for that are not as complicated as they may seem.

Month Names

The names of the months are determined taking into account nakshâtras as well as sankrântis. Every sankrânti was assigned a nakshâtra from which the name of the month was derived. The months were given the name according to the last sankrânti before the new moon of the respective lunation following the table below. The lunation with the new moon occuring after the Mîna-sankrânti (and, therefore, before the Mesha-sankrânti) is called Chaitra. The lunation with the new moon between Mesha-sankrânti and Vrishabha-sankrânti Vaishâkha etc. The table shows seasons, names and sequence of the months and the sankrânti before the respective lunation's new moon.

In southern India months end with the new moon, whereas in northern India months are beginning end ending with new moons.

Intercalation

From the rules for assigning names to months a pattern for insertion or omission of leap months follows. The time it takes the (notional) sun to pass a sankrânti interferes in one of the following ways with the synodic month: -

The result of these rules is a leap year pattern similar to that of the Metonic cycle.

Designation of Days

The solar calendar simply designates days within months by their number. In lunisolar calendars a more complicated system is employed. Single days can be inserted or left out.

A lunar month consists of 30 tithis which are numbered within a half month (paksha) from 1 to 15. A day is designated with the number of the tithi in which the sunrise of that day occurs. In most cases, this leads to a "normal" sequence of numbers though occasionally there are tithi numbers omitted (kshaya-tithi) or repeated (adhika-tithi) for reasons similar to the rules for inter-/extracalating months. Numbers are more frequently omitted than repeated because the mean tithi length is shorter than that of a solar day(3).

Beginning of the Year

There are different customs for fixing the beginning of a new year. In some areas the year is begun with Chaitra, in others with Kârttika. Furthermore, different beginnings of the month are in use. In south India the month begins with the day after new moon mainly, whereas in the north full moon day is considered to be the first day of a new month.

Unlike the Islamic calendar, these lunisolar calendars are not observation-based. Obviously profound astronomical knowledge is necessary for the pre-computation of such a calendar. There is a great variety in the actual implementation of the calendars described here. The transformation if historic dates in most cases can be done only with an accuracy of within a month.

Solar Calendar

Solar calendars are in use in India since the 4th century CE and came to India from the Hellenistic world. The lunar calendars were not replaced by the solar ones though, and the solar date was mentioned alongside the lunar date to avoid misinterpretations. The Indian solar calendars are based on the sidereal year unlike most of the other solar calendars using the tropical year. Although the astronomers in ancient India were aware of the slow precession of the vernal equinox the solar calendars were never adjusted.

The months take their names from the zodiacal signs and have varying mean lengths due to the inconstant apparent movement of the sun throughout the year. The table below shows sequence, names, and mean lengths of the months. However, there are regional variations.

* There are slightly differing values in the siddhântas.

Every month begins with the day of the first sunrise after the notional beginning of the month.

Indian National Calendar

In the 1950s, the Indian government tried to introduce a reformed calendar with a basic structure similar to the Gregorian calendar. The months were given the names of the traditional solar calendar months and fixed lengths. The leap year pattern was adjusted to the Gregorian calendar. Names, sequence, and lengths of the months can be seen in the following table.

New Year, i. e. 1 Chaitra, falls on 22 March in common years, on 21 March in leap years. Thus, a certain Indian national calendar date corresponds to a certain Gregorian calendar date except of the period from 10 Phâlguna to 21 Vaishâkha, or 29 February to 20 April (inclusively) in which the Indian national calendar date is one higher in leap years. The year is 77 (before 21/22 March) or 78 less than the Gregorian year.

This calendar could not replace the many calendars used in India, and the Gregorian calendar is employed for dating newspapers or documents. Holidays are determined according to the tradional calendars.

Year Counts and Epochsr

A sequential numbering of years is not documented until the 1st century BCE. If the year was specified at all, regnal years of the respective ruler or king were used. The growing influences from Europe and China the concept of counting years from a certain era came to India with the result of many different eras.

The Vikrama era (58 BCE) takes its name from a so far unidentified king Vikramâditya who is said to have driven the Shaka out of Ujjayinî, a town in northern India. King Chandra Gupta II bore the title Vikramâditya and freed Ujjayinî from the Shaka ruled about 400 years later.

The Shaka era begins in 78 CE and is said to have been founded by a Shaka who re-conquered Ujjayinî 137 years after Vikramâditya. This era was used first in western India (Mâlwâ, Kâthiâwâr und Gujarât) and later spread over the whole Indian subcontinent and to South East Asia. It is also the era of the Indian national calendar.

For certain periods fo time other eras were popular, e. g. the Gupta, Harsha, and the Kalachuri eras. See also Epochs and Eras.