The Hindu calendar used in Vedic times has undergone many changes in the process of regionalization, and today there are several regional Indian calendars, as well as an Indian national calendar. Mostly, these are inherited from a system first enunciated in Jyotish Vedanga (one of the six adjuncts to the Vedas, 12th to 14th century BC), standardized in the Surya Siddhanta (3rd century) and subsequently reformed by astronomers such as Aryabhata (499), Varahamihira (6th century) Bhaskara (12th century), and Fatehullah Shirazi (16th century). There are differences and regional variations abound in these computations, but the following is a general overview.

Basic structure

There are two types of Hindu calendar:

1. the solar calendar or the saura māna
2. the lunisolar calendar or the chāndra māna

The structure of the Hindu calendar is of course composed of days making months making years. The system of describing days is the same in both the solar and lunisolar calendars. The system of describing months and hence years is what distinguishes the solar and lunisolar calendars from each other. This article first describes the day, then the months and year of the solar calendar, and then the months and year of the lunisolar calendar. Then it discusses the year numbering and the 60 names of the years.

Day

The Hindu calendrical day starts with local sunrise. It is allotted five "properties", called anga-s. They are:

1. the tithi active at sunrise
2. the vaasara or weekday
3. the nakshatra in which the moon resides at sunrise
4. the yoga active at sunrise
5. the karana active at sunrise.

Together these are called the panchānga-s where pancha means "five" in Sanskrit. An explanation of the terms follows.

Tithi

The (anticlockwise) angular distance between the sun and moon as measured from the earth along the ecliptic (circle on the sky in which the sun, moon and planets seem to move) can vary between 0° and 360°. This is divided into 30 parts. Each part ends at 12°, 24° etc. The time spent by the moon in each of these parts (i.e. the time taken for the angular distance to increase

The month has two paksha-s or fortnights. The first 15 tithi-s constitute the bright fortnight or shukla paksha and the next 15 tithi-s constitute the dark fortnight or krishna paksha. tithi-s are indicated by their paksha and ordinal number within the paksha. The 15th tithi of the bright fortnight (full moon) is called pūrnimā and the 15th tithi of the dark fortnight (new moon) is called amāvāsyā.

The tithi in which the moon is at the time of sunrise of a day is taken to be the tithi for the day.

Vaasara

The weekdays are as usual seven. They are (starting from Sunday):

1. Indu vāsara
2. Soma vāsara
3. Mangala vāsara
4. Budha vāsara
5. Guru vāsara
6. Shukra vāsara
7. Shani vāsara

There are many other variations of these names, using other names of the celestial bodies of the Sun, Moon, Mars, Mercury, Jupiter, Venus and Saturn. The word vāsara means "weekday". In common language, the word 'vaasara' is replaced by 'vaara', so Friday is 'Shukravaara' etc.

Nakshatra

The ecliptic is divided into 27 nakshatra-s, which are variously called lunar houses or asterisms. These reflect the moon's cycle against the fixed stars, 27 days and 7¾ hours. Nakshatra computation appears to have been well known at the time of the Rig Veda (2nd–1st millennium BC).

The starting point for this division is the point on the ecliptic directly opposite to the star Spica called Chitrā in Sanskrit. (Other slightly-different definitions exist.) It is called Meshādi or the "start of Aries". The ecliptic is divided into the nakshatra-s eastwards starting from this point.

The names of the nakshatra-s are given below. As always, there are many versions with minor differences. The names on the right-hand column give roughly the correspondence of the nakshatra-s to modern names of stars. Note that nakshatra-s are (in this context) not just single stars but are segments on the ecliptic characterised by one or more stars. Hence you will find many stars mentioned for one nakshatra.

An additional 28th intercalary nakshatra, Abhijit (alpha, epsilon and zeta Lyrae - Vega - between Uttarasharha and Sravana), is required to compensate for the sidereal month being eight hours more than 27 days. Unlike the 13°20' range of the 27 proper nakshatras, Abhijit spans 4°14' to reflect the extra span of 7¾ hours.

The nakshatra in which the moon lies at the time of sunrise of a day is the nakshatra for the day.

Yoga

First, the angular distance along the ecliptic of any object on the sky, measured from Meshādi (as defined above) is called the longitude of that object. When the longitude of the sun and the longitude of the moon are added, they produce a value ranging from 0° to 360°. (Values greater than or equal to 360° must be reduced to less than 360° by subtracting 360°.) This is divided into 27 parts. Each part will now equal 800' (where ' is the symbol of the arcminute which means 1/60 of a degree.) These parts are called the yoga-s. They are labeled:

1. Vishkambha
2. Prīti
3. Āyushmān
4. Saubhāgya
5. Shobhana
6. Atiganda
7. Sukarman
8. Dhriti
9. Shūla
10. Ganda
11. Vriddhi
12. Dhruva
13. Vyāghāta
14. Harshana
15. Vajra
16. Siddhi
17. Vyatīpāta
18. Varigha
19. Parigha
20. Shiva
21. Siddha
22. Sādhya
23. Shubha
24. Shukla
25. Brāhma
26. Māhendra
27. Vaidhriti

Again, minor variations may exist. The yoga that is active during sunrise of a day is the yoga for the day.

Karana

A karana is half of a tithi. To be precise, a karana is the time required for the angular distance between the sun and the moon to increase

Since the tithi-s are thirty in number, one would expect there to be sixty karana-s. But there are only eleven. There are four "fixed" karana-s and seven "repeating" karana-s. The four "fixed" karana-s are:

1. Kimstughna
2. Shakuni
3. Chatushpād
4. Nāgava

The seven "repeating" karana-s are:

1. Bava
2. Bālava
3. Kaulava
4. Taitula
5. Garajā
6. Vanijā
7. Vishti (Bhadrā)

• Now the first half of the first tithi (of the bright fortnight) is always Kimstughna karana. Hence this karana is "fixed".
• Next, the seven repeating karana-s repeat eight times to cover the next 56 half-tithi-s. Thus these are the "repeating" karana-s.
• The three remaining half-tithi-s take the remaining "fixed" karana-s in order. Thus these are also "fixed".
• Thus one gets sixty karana-s from eleven.

The karana active during sunrise of a day is the karana for the day.

Month and year of the solar calendar

Now that the days are defined, we shall speak of how the solar calendar reckons its months and year.

As has been previously noted, the sun is observed to travel along the ecliptic. The ecliptic is now divided into twelve parts called rāshi-s, starting from the point of Meshādi defined above and moving eastwards. The names of the rāshis correspond to those in the West, and may indicate a common Sumerian origin. Greek astronomical interchange, as in the Romaka Siddhanta, also led to a degree of homogenization. This table lists the rāshis along with their zodiac equivalents:

The day on which the sun transits into each rāshi before sunset is taken to be the first day of the month. In case the sun transits into a rāshi after a sunset but before the next sunrise, then the next day is the first day of the month. (Minor variations on this definition exist.)

The days are then labeled 1, 2, 3…. till the first day of the next month.

Thus we get twelve months with varying lengths of 29 to 32 days. This variation in length occurs because the earth's orbit around the sun is an ellipse, but also because of some variability in the transit point falling before or after sunrise. The months are named by the rāshi in which the sun travels in that month.

The new year day is the first day of the month of Mesha. Currently, it occurs around April 15th on the Gregorian calendar.

This is the structure of the Hindu solar calendar.

Months of the lunisolar calendar

When a new moon occurs before sunrise on a day, that day is said to be the first day of the lunar month. So it is evident that the end of the lunar month will coincide with a new moon. A lunar month has 29 or 30 days (according to the movement of the moon).

The tithi at sunrise of a day is the only label of the day. There is no running day number from the first day to the last day of the month. This has some unique results, as explained below:

Sometimes two successive days have the same tithi. In such a case, the latter is called an adhika tithi where adhika means "extra". Sometimes, one tithi may never touch a sunrise, and hence no day will be labeled by that tithi. It is then said to be a tithi kshaya where kshaya means "loss".

Naming lunar months

There are twelve lunar month names:

1. Chaitra
2. Vaishākha
3. Jyaishtha
4. Āshādha
5. Shrāvana
6. Bhādrapada
7. Āshwina
8. Kārtika
9. Mārgashīrsha
10. Pausha
11. Māgha
12. Phālguna

Determining which name a lunar month takes is somewhat indirect. It is based on the rāshi into which the sun transits within a lunar month, i.e. before the new moon ending the month.

There are twelve rāshi names, there are twelve lunar month names. When the sun transits into the Mesha rāshi in a lunar month, then the name of the lunar month is Chaitra. When the sun transits into Vrishabha, then the lunar month is Vaishākha. So on.

The Sanskrit grammatical derivation of the lunar month names Chaitra etc is: the (lunar) month which has its central full moon occurring at or near the nakshatra Chitrā is called Chaitra. Similarly, for the nakshatra-s Vishākhā, Jyeshthā, (Pūrva) Ashādhā, Shravana, Bhādrapada, Ashvinī (old name Ashvayuj), Krittikā, Mrigashīrsha, Pushya, Maghā and (Pūrva/Uttara) Phalgunī the names Vaishākha etc are derived.

The lunar months are split into two pakshas of 15 days. The waxing paksha is called shuklapaksha, light half, and the waning paksha the krishnapaksha, dark half. There are two different systems for making the lunar calendar:

• amanta or mukhya mana system - a month begins with a new moon, mostly followed in the southern states
• purnimanta or gauna mana system - a month begins with a full moon, followed more in the North.

Extra Months

When the sun does not at all transit into any rāshi but simply keeps moving within a rāshi in a lunar month (i.e. before a new moon), then that lunar month will be named according to the first upcoming transit. It will also take the epithet of adhika or "extra". For example, if a lunar month elapsed without a solar transit and the next transit is into Mesha, then this month without transit is labeled adhika Chaitra. The next month will be labeled according to its transit as usual and will get the epithet nija ("original") or shuddha ("clean").

An adhika māsa occurs once every two or three years (meaning, with a gap of one or two years without adhika māsa-s).

Lost Months

If the sun transits into two rāshi-s within a lunar month, then the month will have to be labeled by both transits and will take the epithet kshaya or "loss". There is considered to be a "loss" because: if the sun had transited into only one raashi in a lunar month as is usual, there would have been two separate months labeled by the two transits in question; but now there is only one month labeled by both transits!

For example, if the sun transits into Mesha and Vrishabha in a lunar month, then it will be called Chaitra-Vaishaakha kshaya. There will be no separate months labeled Chaitra and Vaishākha.

A kshaya māsa occurs very rarely. Known gaps between occurrence of kshaya māsa-s are 19 and 141 years. The last was in 1983. Jan-15 through Feb-12 were Pausha-Māgha kshaya. Feb-13 onwards was (adhika) Phālguna.

Special Case:

If there is no solar transit in one lunar month but there are two transits in the next lunar month,

• the first month will be labeled by the first transit of the second month (as usual) and take the epithet adhika and
• the next month will be labeled
  
  
  
  by both its transits as is usual for a kshaya māsa.

This is a very very rare occurrence. The last was in 1315. Oct-08 to Nov-05 were adhika Kārtika. Nov-06 to Dec-05 were Kārtika-Māgashīrsha kshaya. Dec-06 onwards was Pausha.

Religious observances in case of extra and lost months

Among normal months, adhika months, and kshaya months, the earlier are considered "better" for religious purposes. That means, if a festival should fall on the 10th tithi of the Āshvayuja month (this is called Vijayadashamī) and there are two Āshvayuja months caused by the existence of an adhika Āshvayuja, the first adhika month will not see the festival, and the festival will be observed only in the second nija month. However, if the second month is āshvayuja kshaya then the festival will be observed in the first adhika month itself.

When two months are rolled into one in the case of a kshaya māsa, the festivals of both months will also be rolled into this kshaya māsa. For example, the festival of Mahāshivarātri which is to be observed on the fourteenth tithi of the Māgha krishna paksha was, in 1983 CE, observed on the corresponding tithi of Pausha-Māgha kshaya krishna paksha, since in that year, Pausha and Māgha were rolled into one, as we mentioned above.

Year of the lunisolar calendar

The new year day is the first day of the shukla paksha of Chaitra. In the case of adhika or kshaya months relating to Chaitra, the aforementioned religious rules apply giving rise to the following results:

• If an adhika Chaitra is followed by a nija Chaitra, the new year starts with the nija Chaitra.
• If an adhika Chaitra is followed by a Chaitra-Vaishākha kshaya, the new year starts with the adhika Chaitra.
• If a Chaitra-Vaishākha kshaya occurs with no adhika Chaitra before it, then it starts the new year.
• If a Phālguna-Chaitra kshaya occurs, it starts the new year.

Another kind of lunisolar calendar

There is another kind of lunisolar calendar which differs from the former in the way the months are named. This section describes the differences involved, and may be skipped if the article is already too complicated for the reader. It is only included for completeness.

When a full moon (instead of new moon) occurs before sunrise on a day, that day is said to be the first day of the lunar month. In this case, the end of the lunar month will coincide with a full moon. This is called the pūrnimānta māna or "full-moon-ending reckoning", as against the amānta māna or "new-moon-ending reckoning" used before.

This definition leads to a lot of complications:

• The first paksha of the month will be krishna and the second will be shukla.

• The new year is still on the first day of the Chaitra shukla paksha. The next paksha-s will be the Vaishākha krishna, Vaishākha shukla, Jyaishtha krishna and so on, till Phālguna krishna, Phālguna shukla and Chaitra krishna, which is now the last paksha of the year.

• The shukla paksha of a given month, say Chaitra, comprises of the same actual days in both systems, as can be deduces from a careful analysis of the rules. However, the Chaitra krishna paksha-s defined by the two systems will be on different days, since the Chaitra krishna paksha precedes the Chaitra shukla paksha is the pūrnimānta system but follows it in the amānta system.

• Though the regular months are defined by the full moon, the adhika and kshaya lunar months are still defined by the new moon. That is, even if the pūrnimānta system is followed, adhika or kshaya months will start with the first sunrise after the new moon, and end with the new moon.

• The adhika month will therefore get sandwiched between the two paksha-s of the nija months. For example, a Shrāvana adhika māsa will be inserted as follows:
  1. nija Shrāvana krishna paksha
  2. adhika Shrāvana shukla paksha
  3. adhika Shrāvana krishna paksha and
  4. nija Shrāvana shukla paksha
     after which Bhādrapada krishna paksha will come as usual.

• If there is an adhika Chaitra, then it will follow the (nija) Chaitra krishna paksha at the end of the year. Only with the nija Chaitra shukla paksha will the new year start. The only exception is when it is followed by a kshaya, and that will be mentioned later.

• The kshaya month is more complicated. If in the amānta system there is a Pausha-Māgha kshaya, then in the pūrnimānta system there will be the following paksha-s:
  1. Pausha krishna paksha
  2. Pausha-Maagha kshaya shukla paksha
  3. Maagha-Phaalguna kshaya krishna paksha and a
  4. Phālguna shukla paksha.

• The special kshaya case where an adhika māsa precedes a kshaya māsa gets even more convoluted. First, we should remember that the Āshvayuja shukla paksha is the same in both the systems. After this come the following paksha-s:
  1. nija Kārtika krishna paksha
  2. adhika Kārtika shukla paksha
  3. adhika Kārtika krishna paksha
  4. Kārtika-Māgashīrsha kshaya shukla paksha
  5. Māgashīrsha-Pausha kshaya krishna paksha
  6. Pausha shukla paksha
     followed by the Māgha krishna paksha etc as usual.

• The considerations for the new year are:
  1. If there is a Chaitra-Vaishākha kshaya shukla paksha:
     1. if an adhika Chaitra precedes it, then the adhika Chaitra shukla paksha starts the new year
     2. if not, the kshaya shukla paksha starts the new year
  2. If there is a Phālguna-Chaitra kshaya shukla paksha then it starts the new year

It must be noted, however, that none of these above complications cause a change in the day of religious observances. Since only the name of the krishna paksha-s of the months will change in the two systems, festivals which fall on the krishna paksha will be defined by the appropriate changed name. That is, the Mahāshivarātri, defined in the amānta māna to be observed on the fourteenth of the Māgha krishna paksha will now (in the pūrnimānta māna) be defined by the Phālguna krishna paksha.

Correspondence of the lunisolar calendar to the solar calendar

A lunisolar calendar is always a calendar based on the moon's celestial motion, which in a way keeps itself close to a solar calendar based on the sun's (apparent) celestial motion. That is, the lunisolar calendar's new year is to kept always close (within certain limits) to a solar calendar's new year.

Since the Hindu lunar month names are based on solar transits, and the month of Chaitra will, as defined above, always be close to the solar month of Mesha, the Hindu lunisolar calendar will always keep in track with the Hindu solar calendar.

Year numbering

The epoch (starting point or first day of the first year) of the current era of Hindu calendar (both solar and lunisolar) is BCE 3102 January 23 on the proleptic Gregorian calendar (i.e. the Gregorian calendar extended back in time before its promulgation from 1582 October 15). Both the solar and lunisolar calendars started on this date. After that, each year is labeled by the number of years elapsed since the epoch.

This is a unique feature of the Hindu calendar. All other systems use the current ordinal number of the year as the year label. But just as a person's true age is measured by the number of years that have elapsed starting from the date of the person's birth, the Hindu calendar measures the number of years elapsed. As of May 18, 2005, 5106 years have elapsed in the Hindu calendar, so this is the 5107^th Hindu calendar year. Note that the lunisolar calendar year will usually start earlier than the solar calendar year.

Other systems of numbering the Hindu years can be read about at the Samvat article.

Year names

Apart from the numbering system outlined above, there is also a cycle of 60 calendar year names, which started at the first year (at elapsed years zero) and runs continuously:

1. Prabhava
2. Vibhava
3. Shukla
4. Pramoda
5. Prajāpati
6. Āngirasa
7. Shrīmukha
8. Bhāva
9. Yuvan
10. Dhātri
11. Īshvara
12. Bahudhānya
13. Pramāthin
14. Vikrama
15. Vrisha
16. Chitrabhānu
17. Svabhānu
18. Tārana
19. Pārthiva (the current Hindu year 2005-2006 CE carries this name)
20. Vyaya
21. Sarvajit
22. Sarvadhārin
23. Virodhin
24. Vikrita
25. Khara
26. Nandana
27. Vijaya
28. Jaya
29. Manmatha
30. Durmukha
31. Hemalambin
32. Vilambin
33. Vikārin
34. Shārvari
35. Plava
36. Shubhakrit
37. Shobhana
38. Krodhin
39. Vishvāvasu
40. Parābhava
41. Plavanga
42. Kīlaka
43. Saumya
44. Sādhārana
45. Virodhikrit
46. Paritāpin
47. Pramādin
48. Ānanda
49. Rākshasa
50. Nala
51. Pingala
52. Kālayukti
53. Siddhārthin
54. Raudra
55. Durmati
56. Dundubhi
57. Rudhirodgārin
58. Raktāksha
59. Krodhana
60. Kshaya

Eras

Hindu mythology speaks of four eras or ages, of which we are currently in the last. The four are:

1. Krita Yuga or Satya Yuga
2. Tretā Yuga
3. Dvāpara Yuga
4. Kali Yuga

They are often translated into English as the golden, silver, bronze and iron ages. (Yuga means era or age.) It is believed that the ages see a gradual decline of dharma, wisdom, knowledge, intellectual capability, life span and emotional and physical strength. The epoch provided above is the start of the Kali Yuga. The Kali Yuga is 432,000 years long. The Dvāpara, Tretā and Krita (Satya) Yuga-s are said to be twice, thrice and four time the length of the Kali Yuga respectively. Thus they together constitute 4,320,000 years. This is called a Chaturyuga. An interesting comparison can be made to Hesiod's Ages of Man Gold, Silver, Bronze, Heroes, and Iron from Greek mythology.

A thousand and a thousand (i.e. two thousand) chaturyuga-s are said to be one day and night of the creator Brahmā. He (the creator) lives for 100 years of 360 such days and at the end, he is said to dissolve, along with his entire Creation, into the Eternal Soul or Paramātman.

A different view of the timespan of a yuga is given by Swami Sri Yukteswar Giri, the guru of Paramahansa Yogananda. This is detailed in his book, The Holy Science. According to this view, the chaturyuga spans a much lower timespan, on the order of thousands of years, and moves cyclically. According to calculations given in the book, the most recent yuga change was in 1800, when the Earth passed from Kali Yuga to Dvāpara Yuga. We are in an ascending spiral right now, and will pass into the Tretā Yuga in a few centuries. According to the book, the quality of human intellect depends on the distance of the Sun from the galactic core and other powerful stars. In the book, the core of the galaxy is called Vishnunābhi, or the navel of Vishnu. The closer the Sun is to it, the more energy the Solar System receives, and the greater is the level of human spiritual and overall development.

History

The Hindu Calendar descends from the Vedic times. There are many references to calendrics in the Vedas. The Vedānga (adjunct to Veda) called Jyautisha (literally, "celestial body study") prescribed all the aspects of the Hindu calendars. After the Vedic period, there were many scholars such as Āryabhata (5th century), Varāhamihira (6th century) and Bhāskara (12th century) who were experts in Jyautisha and contributed to the development of the Hindu Calendar.

The most widely used authoritative text for the Hindu Calendars in the Sūrya Siddhānta, a text of uncertain age, though some place it at 10th century.

The traditional Vedic calendar used to start with the month of agrahayan (agra=first + ayan = travel of the sun, equinox) or Mārgashirshe. This is the month where the Sun crosses the equator, i.e. the vernal equinox. This month was called mārgashirshe after the fifth nakshatra (around lambda orionis). Due to the precession of the earth's axis, the vernal equinox is now in Pisces, and corresponds to the month of chaitra. This shift over the years is what has led to various calendar reforms in different regions to assert different months as the start month for the year. Thus, some calendars (e.g. Vikram) start with Chaitra, which is the present-day month of the vernal equinox, as the first month. Others may start with Vaisakha (e.g. Bangabda). The shift in the vernal equinox by nearly four months from agrahaayana to chaitra in sidereal terms seems to indicate that the original naming conventions may date to the fourth or fifth millennium BC, since the period of precession in the earth's axis is about 25,800 years.

Regional Variants

The two calendars most widely used in India today are the Vikram calendar followed in North India while South Indian states such as Karnataka, Andhra Pradesh and Tamil Nadu follow the Shalivahana calendar. A variant of the Vikram Calendar, was reformed and standardized as the Indian National calendar in 1957 to have constant days in every month (with leap years). Years are counted from 78, year zero of the Saka era. The Bengal Calendar, Bangabda (introduced 1584) is widely used in Eastern India. A reformed version of this calendar, with constant days in each month and a leap year system (1966) serves as the national calendar for Bangladesh. Nepal also follows the Vikram calendar. The same month names and roughly the same periods apply to a number of Buddhist calendars in Sri Lanka, Tibet and other areas.

As an indicator of this variation, 'Whitaker’s Almanac' reports that the The Gregorian year 2000 AD corresponds, respectively with:

1. Year 6001 in the Kaliyuga calendar;
2. Year 2544 in the Buddha Nirvana calendar;
3. Year 2057 in the Vikram Samvat calendar;
4. Year 1922 in the Saka calendar;
5. Year 1921 (shown in terms of 5-yearly cycles) of the Vedanga Jyotisa calendar;
6. Year 1407 in the Bengali San calendar;
7. Year 1176 in the Kollam calendar.

The Indian Calendar Reform Committee, appointed in 1952 (shortly after Indian independence), identified more than thirty well-developed calendars, allvariants of the Surya Siddhanta calendar outlined here, in systematic use across different parts of India.

Further reading

• Reingold and Dershowitz, Calendrical Calculations, Millennium Edition, Cambridge University Press, latest 2nd edition 3rd printing released November 2004. ISBN 0-521-77752-6
• A.L. Basham, The Wonder that was India, Appendix II: "Astronomy", Macmillan, 1954. Rupa and Co, Calcutta, reprint.
• S. Balachandra Rao, Indian Astronomy: An Introduction, Universities Press, Hyderabad, 2000.

See also

• Indian national calendar
• Jyotish
• Metrics of time in Hinduism
• Samvat
• Bangla Calendar

Calendrier sayana 印度曆