Notes on Indian Calendars

The 3 major Calendar types

There are three major classification of Indian calendar. The Solar calendar, the Lunar calendar and the Savana calendar. The solar calendar is based on the movement of the Sun while the Lunar calendar is based on the relative movement of the Moon “with regards” to the Sun. Because the movement of the Moon is seen with reference to the Sun, it is also called Soli-lunar calendar. The Savana calendar is also called the civil calendar and is based on two successive Sunrises, Noons, Sunsets, or Midnights. Unlike Solar and Soli-lunar calendar, there is no astronomical basis for the Savana Calendar and has been devised, not to keep track of astronomical events, but to regulate time in the day to day life of people. It is based on an assumption that a year is 360 days long having 12 months with 30 days each.

Although the Solar and the Lunar calendar are different, the common theme behind them is the usage of sidereal zodiac (narayana chakra) for tracking the movement of the luminaries. In the solar calendar, the duration of a day is equivalent to 1 degree movement of the Sun in the zodiac while in the Lunar calendar, the duration of a day is equivalent to a Tithi or (lunar day) which is 12 degree relative movement of Moon from the Sun.

The beginning of the year in the Solar calendar is reckoned by looking at the entry of the Sun in the first sign of the zodiac i.e., Aries which at current times happen around mid-April. This marks the first month of Vaishakha in most part of India and Chaitra in Tamil Nadu. In my personal opinion Tamil naming of the month is more apt as Chaitra is derived from Chitra which falls in exact opposite to the beginning of Aries. In north Indian Solar calendar, the month of Chaitra falls when Sun enters Pisces. Here, the name Chaitra corresponds to a point which falls end of the Solar month and opposite to zodiac Chitra nakshatra. The reason of shifting the month name backward by one perhaps is to synchronise with the Amanta Lunar calendar.

The Lunar calendar has two important variations. The Amanta (ending with Amavasya) is the most prevalent reckoning and is called Mukyamana (main reckoning). On the other hand the Shuklanta (ending with Purnima) is less prevalent and is used in some north Indian states is called Gauna mana (secondary reckoning).

The Amanta year starts with Sun-Moon conjunction in Sidereal Pisces, which goes by the name Chaitra. The reason behind the name is that, assuming that the month starts with Sun-Moon conjunction in middle of Pisces, then during the mid of the Chaitra month which will fall on a Purnima, the Moon will be in the Chitra Nakshatra.

The Shuklanta Year starts at the same time as the amanta Year but it starts in the middle of the first month of Chaitra which coincides with an Amavashya. Thus the 1st month of Chaitra in this calendar starts about a fortnight (1 paksha) before the year start, with Shukla Pratipada (1st day in bright half). Which means that in Shuklanta Calendart, the Chaitra Month starts one paksha before the Beginning of the year, which may sound somewhat awkward. One can say that the year starts on 15th of the Chaitra month in the Shuklanta Calendar. This means that the 1st month of the calendar has only 15 days lunar days (tithis).

The month of both the Lunar Calendars overlap by one paksha (fortnight) which coincides with the 1st half of Amanta calendar and 2nd half of Shuklanta Calendar. This happens in the bright half or the Shukla Paksha. Thus the bright half of the amanta and shuklanta months will share the same name. Regarding the dark half (Krsna paksha), the Amanta month will always start about 15 days (one paksha or fortnight) later than the Shuklanta Month.

Year Numbering and Naming

The years are also called the Samvatsara or Abda. The Vatsara or the Varsha are derived from Samvatsara. The Samvatsaras are the cycles of 60 years as per the Jupiter-Saturn cycle. Although the years bear the same names as the Jovian cycle, the starting point of the year can vary. It is prevalent to reckon the names of the Samvatsara based on either (1) the Sun’s entry into Aries or (2) Sun-Moon conjunction in Pisces (if 2 Sun-Moon conjunctions happen in Pisces, then the 2nd one is considered).

Many different eras are followed in India, and based on which different year numbers can be assigned. The common eras are (1) Saka era (Sak Samvat), (2) Vikrama era (Vikram Samvat) and the (3) Kali era.

The Saka Samvat / Saka Era / Saka Epoch

The Saka era started in 78 AD coinciding with Sun-Moon conjunction in Pisces (Lunar Calendar) or Sun’s entry into Aries (Solar Calendar). The way to convert the year number from Gregorian epoch to Saka epoch is to subtract 78 from Gregorian year if Sun is in Aries to middle of Capricorn (since Gregorian year starts with Jan 1 when Sun is about in the middle of Capricorn (10 degree 14 min currently which will change due to precision of equinox).

In summary, the formula is-

Saka Year =

• Before Indian Calendar Year start, Saka year (Jan 1st to Chaitra Shukla Pratipad) = Gregorian year — 79
• After Indian Calendar Year start, Saka Year (Chaitra Shukla Pratipada to Dec 31st) = Gregorian year — 78

The Vikram Samvat/ Vikram Era / Vikram Epoch

Once the Saka year is determined, the Vikram Samvat can be determined by applying a correction to the Saka year. To understand the correction we need to know when the Vikram era was initiated. History tells us that in the year 56 BC, Vikrama Samvat era was founded by the emperor Vikramaditya of Ujjain following his victory over the Sakas.

Later, in a similar fashion, Satavahana king Gautamiputra Satakarni initiated the Saka era to celebrate his victory against the Sakas in the year AD 78.

So Vikram era = Gregorian era + 57 = Saka era + 135.

This means that the Vikram Epoch started 135 years before Saka Epoch and 57 years before the Gregorian Epoch. On the other hand, the Saka era started 78 years after the Gregorian Epoch.

Samvatsara Name

To determine the name of the Samvatsara, we need to determine the index of the year in the Epoch. The Samvatsara year index can be derived from in various era using the following formula:

• Saka Era: Reminder of (Saka year — 48 ) / 60
• Vikrama Era: Reminder of (Vikrama year — 3)/ 60

Why are we subtracting 48 and 3 respectively from the Saka and Vikram Era? Because, in the Saka Epoch, 48 Samvatsara is yet to elapse when the epoch started. Similarly, in the Vikram Epoch, 3 Samvatsara is yet elapse. This can also be put in this way. 48th year from the start of Saka Epoch will be last year of the 60 years Samvatsara cycle. Similarly, 3rd year from the start of Vikram Epoch will be the last year of the 60 years cycle.

The Index can be found from Gregorian Epoch using the following formula.

• Before Indian year start date: (Gregorian year — 7)/ 60
• After Indian year start date: (Gregorian year — 6)/ 60

The Samvatsara in the 1st year in various Epochs:

1. Saka era 1st year = 13th Samvatsara: Pramathi = 78 AD Gregorian year
2. Vikrama era 1st year = 58th Samvatsara: Raktakshin = 57 BC (-56) Proleptic Gregorian year
3. Gregorian 1st year = 55th Samvatsara: Durmati = -77 Saka era = 58 Vikrama era

The 60 Samvatsara names are:

1.Prabhava, 2. Vibhava, 3. Śukla, 4. Pramodadūta, 5. Prajāpati, 6. Āṅgīrasa, 7. Śrīmukha, 8. Bhāva, 9. Yuva, 10. Dhātṛ, 11. Īśvara, 12. Bahudhānya

13.Pramāthi, 14. Vikrama, 15. Vṛṣa, 16. Chitrabhānu, 17. Subhānu, 18. Tāraṇa, 19. Pārthiva, 20. Vyaya, 21. Sarvajit, 22. Sarvadhārin, 23. Virodhin, 24. Vikṛti

25.Khara, 26. Nandana, 27. Vijaya, 28. Jaya, 29. Manmatha, 30. Durmukha, 31. Hemalambin, 32. Vilambin, 33. Vikārin, 34. Śārvarin, 35. Plava, 36. Śubhakṛt

37.Śobhana, 38. Krodhin, 39. Viśvāvasu, 40. Parābhava, 41. Plavaṅga, 42. Kīlaka, 43. Saumya, 44. Sādhāraṇa, 45. Virodhakṛt, 46. Paridhāvin, 47. Pramādin, 48. Ānanda

49.Rākṣasa, 50. Nala/Anala, 51. Piṅgala, 52. Kālayukta, 53. Siddhārthin, 54. Raudra, 55. Durmati, 56. Dundubhi, 57. Rudhirodgārin, 58. Raktākṣin, 59. Krodhana/Manyu, 60. Kṣaya