Hindu calendar

Later, the term Jyotisha evolved to include Hindu astrology. The astrological application of the Hindu calendar was a field that likely developed in the centuries after the arrival of Greek astrology with Alexander the Great,[20][32][33] because their zodiac signs are nearly identical.[17][34]

The ancient Hindu texts on Jyotisha only discuss timekeeping, and never mention astrology or prophecy.[35] These ancient texts predominantly cover astronomy, but at a rudimentary level.[18] Later medieval era texts such as the Yavana-jataka and the Siddhanta texts are more astrology-related.[36]

Hinduism and Buddhism were the prominent religions of southeast Asia in the 1st millennium CE, prior to the Islamic conquest that started in the 14th century. The Hindus prevailed in Bali, Indonesia, and they have two types of Hindu calendar. One is a 210-day based Pawukon calendar which likely is a pre-Hindu system, and another is similar to lunisolar calendar system found in South India and it is called the Balinese saka calendar which uses Hindu methodology.[37] The names of month and festivals of Balinese Hindus, for the most part, are different, though the significance and legends have some overlap.[37]

The Hindu calendar divides the zodiac into twelve division called rāśi. The time taken by the Sun to transit through a rāśi is a solar month whose name is identical to the name of the rāśi. In practice, solar months are mostly referred as rāśi (not months).

The solar months are named differently in different regional calendars. While the Malayalam calendar broadly retains the phonetic Sanskrit names, the Bengali and Tamil calendars repurpose the Sanskrit lunar month names (Chaitra, Vaishaka etc.) as follows:

• The Tamil calendar replaces Mesha, Vrisha etc. with Chithirai, Vaigasi etc.
• The Bengali calendar is similar to the Tamil calendar except in that it starts the year with Boiśākh (instead of Choitrô), followed by Jyoisthô etc. The Assamese and Odia calendars too are structured the same way.

The solar months (rāśi) along with their equivalent names in the Bangali, Malayalam and Tamil calendar are given below:

The solar months (rāśi) along with the approximate correspondence to Hindu seasons and Gregorian months are:[30]

The names of the solar months are also used in the Darian calendar for the planet Mars.

Lunar months are defined based on lunar cycles, i.e. the regular occurrence of new moon and full moon and the intervening waxing and waning phases of the moon.

A lunar month contains two fortnights called pakṣa (पक्ष, literally "side").[2] One fortnight is the bright, waxing half where the moon size grows and it ends in the full moon. This is called "Gaura Paksha" or Shukla Paksha.[46] The other half is the darkening, waning fortnight which ends in the new moon. This is called "Vadhya Paksha" or Krishna Paksha.[2] The Hindu festivals typically are either on or the day after the full moon night or the darkest night (amavasya, अमावास्या), except for some associated with Krishna, Durga or Rama. The lunar months of the hot summer and the busy major cropping-related part of the monsoon season typically do not schedule major festivals.[47]

Map of regions in India using Hindu solar (orange),Lunar Amanta (blue), and Lunar Purnimanta(red) Calendars

Two traditions have been followed in the Indian subcontinent with respect to lunar months: the amanta tradition, which ends the lunar month on new moon day (similar to the Islamic calendar) and the purnimanta tradition, which ends it on full moon day.[48] As a consequence, in the amanta tradition, Shukla paksha precedes Krishna paksha in every lunar month, whereas in the purnimanta tradition, Krishna paksha precedes Shukla paksha in every lunar month. As a result, a Shukla paksha will always belong to the same month in both traditions, whereas a Krishna paksha will always be associated with different (but succeeding) months in each tradition.

The amanta (also known as Amavasyanta or Mukhyamana) tradition is followed by most Indian states that have a peninsular coastline (except Assam, West Bengal, Odisha, Tamil Nadu and Kerala, which use their own solar calendars). These states are Gujarat, Maharashtra, Goa, Karnataka, Andhra Pradesh and Telangana. Nepal and most Indian states north of the Vindhya mountains follow the purnimanta (or Gaunamana) tradition.

The purnimanta tradition was being followed in the Vedic era. It was replaced with the amanta tradition as the Hindu calendar system prior to the 1st century BCE, but the Purnimanta tradition was restored in 57 BCE by Vikramaditya, who wanted to return to the Vedic roots.[48] The presence of this system is one of the factors considered in dating ancient Indian manuscripts and epigraphical evidence that have survived into the modern era.[48][49]

The two traditions of Amanta and Purnimanta systems have led to alternate ways of dating any festival or event that occurs in a Krishna paksha in the historic Hindu, Buddhist or Jain literature, and contemporary regional literature or festival calendars. For example, the Hindu festival of Maha Shivaratri falls on the fourteenth lunar day of Magha's Krishna paksha in the Amanta system, while the same exact day is expressed as the fourteenth lunar day of Phalguna's Krishna paksha in the Purnimanta system.[50] Both lunisolar calendar systems are equivalent ways of referring to the same date, and they continue to be in use in different regions, though the Purnimanta system is now typically assumed as implied in modern Indology literature if not otherwise specified.[31][30]

The names of the Hindu months vary by region. Those Hindu calendars which are based on lunar cycle are generally phonetic variants of each other, while the solar cycle are generally variants of each other too, suggesting that the timekeeping knowledge travelled widely across the Indian subcontinent in ancient times.[1][30]

During each lunar month, the Sun transits into a sign of the zodicac (sankranti). The lunar month in which the Sun transits into Mesha is named Chaitra and designated as the first month of the lunar year.

A few major calendars are summarized below:

Twelve Hindu mas (māsa, lunar month) are equal to approximately 354 days, while the length of a sidereal (solar) year is about 365 days. This creates a difference of about eleven days, which is offset every (29.53/10.63) = 2.71 years, or approximately every 32.5 months.[29] Purushottam Maas or Adhik Maas is an extra month that is inserted to keep the lunar and solar calendars aligned. The twelve months are subdivided into six lunar seasons timed with the agriculture cycles, blooming of natural flowers, fall of leaves, and weather. To account for the mismatch between lunar and solar calendar, the Hindu scholars adopted intercalary months, where a particular month just repeated. The choice of this month was not random, but timed to sync back the two calendars to the cycle of agriculture and nature.[29][30]

The repetition of a month created the problem of scheduling festivals, weddings and other social events without repetition and confusion. This was resolved by declaring one month as Shudha (pure, clean, regular, proper, also called Deva month) and the other Mala or Adhika (extra, unclean and inauspicious, also called Asura masa).[51]

The Hindu mathematicians who calculated the best way to adjust the two years, over long periods of a yuga (era, tables calculating 1000 of years), they determined that the best means to intercalate the months is to time the intercalary months on a 19-year cycle, similar to the Metonic cycle used in the Hebrew calendar. This intercalation is generally adopted in the 3rd, 5th, 8th, 11th, 14th, 16th and 19th year of this cycle. Further, the complex rules rule out the repetition of Mārgasirsa (also called Agrahayana), Pausha and Maagha lunar months. The historic Hindu texts are not consistent on these rules, with competing ideas flourishing in the Hindu culture.[52]

The Hindu calendar makes further rare adjustments, over a cycle of centuries, where a certain month is considered kshaya month (dropped). This occurs because of the complexity of the relative lunar, solar and earth movements. Underhill (1991) describes this part of Hindu calendar theory: "when the sun is in perigee, and a lunar month being at its longest, if the new moon immediately precedes a samkranti, then the first of the two lunar months is deleted (called nija or kshaya)." This, for example, happened in the year 1 BCE, when there was no new moon between Makara samkranti and Kumbha samkranti, and the month of Pausha was dropped.[53]

Vāsara refers to the weekdays in Sanskrit.[58] Also referred to as Vara and used as a suffix.[45] The correspondence between the names of the week in Hindu and other Indo-European calendars are exact. This alignment of names probably took place sometime during the 3rd century CE.[59][60] The weekday of a Hindu calendar has been symmetrically divided into 60 ghatika, each ghatika (24 minutes) is divided into 60 pala, each pala (24 seconds) is subdivided into 60 vipala, and so on.[59]

The term -vāsara is often realised as vāra or vaar in Sanskrit-derived and influenced languages. There are many variations of the names in the regional languages, mostly using alternate names of the celestial bodies involved.

The complete Vedic calendars contain five angas or parts of information: lunar day (tithi), solar day (diwas), asterism (naksatra), planetary joining (yoga) and astronomical period (karanam). This structure gives the calendar the name Panchangam.[45] The first two are discussed above.

The Sanskrit word Yoga means "union, joining, attachment", but in astronomical context, this word means latitudinal and longitudinal information. The longitude of the Sun and the longitude of the Moon are added, and normalised to a value ranging between 0° to 360° (if greater than 360, one subtracts 360). This sum 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 yogas. They are labelled:

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

A karaṇa is half of a tithi. To be precise, a karaṇa is the time required for the angular distance between the Sun and the Moon to increase in steps of 6° starting from 0°. (Compare with the definition of a tithi.)

Since the tithis are 30 in number, and since 1 tithi = 2 karaṇas, therefore one would logically expect there to be 60 karaṇas. But there are only 11 such karaṇas which fill up those slots to accommodate for those 30 tithis. There are actually 4 "fixed" (sthira) karaṇas and 7 "repeating" (cara) karaṇas.

The 4 "fixed" karaṇas are:

1. Śakuni (शकुनि)
2. Catuṣpāda (चतुष्पाद)
3. Nāga (नाग)
4. Kiṃstughna (किंस्तुघ्न)

The 7 "repeating" karaṇas are:[62]

1. Vava or Bava (बव)
2. Valava or Bālava (बालव)
3. Kaulava (कौलव)
4. Taitila or Taitula (तैतिल)
5. Gara or Garaja (गरज)
6. Vaṇija (वणिज)
7. Viṣṭi (Bhadra) (भद्रा)

• Now the first half of the 1st tithi (of Śukla Pakṣa) is always Kiṃtughna karaṇa. Hence this karaṇa is "fixed".
• Next, the 7-repeating karaṇas repeat eight times to cover the next 56 half-tithis. Thus these are the "repeating" (cara) karaṇas.
• The 3 remaining half-tithis take the remaining "fixed" karaṇas in order. Thus these are also "fixed" (sthira).
• Thus one gets 60 karaṇas from those 11 preset karaṇas.

The Vedic day begins at sunrise. The karaṇa at sunrise of a particular day shall be the prevailing karaṇa for the whole day. (citation needed )

Nakshatras are divisions of ecliptic, each 13° 20', starting from 0° Aries.

Calendars based on lunar cycle (lunar months in solar year, lunar phase for religious dates and new year):

• Vikram Samvat
  • Vikrami era – North and Central India (Lunar)
  • Gujarati samvat – Gujarat, Rajasthan
  • Sindhi samvat – Sindhis
• Shalivahana calendar (Shaka era) – Used in Deccan region states of Maharashtra, Goa, Karnataka, Andhra Pradesh, Telangana
• Saptarishi era calendar – Kashmiri Pandits
• Nepal Sambat – Nepal, Sikkim
• Meitei calendar – Manipur

Calendars based on solar cycle (solar months in solar year, lunar phase for religious dates but new year which falls on solar date – South and Southeast Asian solar New Year):

• Assamese calendar – Assam
• Bengali calendar – West Bengal
• Odia calendar – Odisha
• Tirhuta Panchang – Maithilis
• Tripuri calendar – Tripura
• Malayalam calendar – Kerala
• Tamil calendar – Tamil Nadu
• Tulu calendar – Tulus
• Vikram Samvat calendar - Nepal
  • Vi– North and Central India (Solar)
  • Bikram Sambat – Nepal, Sikkim

• Indian national calendar – used by Indian Government (civil calendar based on solar months)
• Vira Nirvana Samvat (Lunar) – Jain
• Buddhist calendar (Lunar) – Buddhist
• Tibetan calendar (Lunar) – Tibet, Ladakh, Sikkim, Arunachal Pradesh
• Pawukon calendar – Bali
• Balinese saka calendar (Lunar) – Bali
• Cham calendar (Lunar) – Chams
• Chula Sakarat (Lunar) – Myanmar
• Thai solar calendar – Thailand
• Thai lunar calendar – Thailand
• Khmer calendar (Lunar & Solar) – Cambodia

• Kim Plofker (2009). Mathematics in India. Princeton University Press. ISBN 978-0-691-12067-6.
• Pingree, David (1973). "The Mesopotamian Origin of Early Indian Mathematical Astronomy". Journal for the History of Astronomy. SAGE. 4 (1): 1–12. Bibcode:1973JHA.....4....1P. doi:10.1177/002182867300400102. S2CID 125228353.
• Pingree, David (1981). Jyotihśāstra : Astral and Mathematical Literature. Otto Harrassowitz. ISBN 978-3447021654.
• Yukio Ohashi (1999). Johannes Andersen (ed.). Highlights of Astronomy, Volume 11B. Springer Science. ISBN 978-0-7923-5556-4.
• Yukio Ohashi (1993). "Development of Astronomical Observations in Vedic and post-Vedic India". Indian Journal of History of Science. 28 (3).
• Maurice Winternitz (1963). History of Indian Literature, Volume 1. Motilal Banarsidass. ISBN 978-81-208-0056-4.