Hindu calendar

The Hindu calendar refers to a set of various lunisolar calendars that are traditionally used in the Indian subcontinent and South-east Asia, with further regional variations for social and Hindu religious purposes. They adopt a similar underlying concept for timekeeping based on sidereal year for solar cycle and adjustment of lunar cycles in every three years, however also differ in their relative emphasis to moon cycle or the sun cycle and the names of months and when they consider the New Year to start.[1] Of the various regional calendars, the most studied and known Hindu calendars are the Shalivahana Shaka found in the Deccan region of Southern India, Vikram Samvat (Bikrami) found in Nepal, North and Central regions of India, Tamil calendar used in Tamil Nadu – all of which emphasize the lunar cycle. Their new year starts in spring. In contrast, in regions such as Kerala, the solar cycle is emphasized and this is called the Malayalam calendar, their new year starts in autumn, and these have origins in the second half of the 1st millennium CE.[1][2] A Hindu calendar is sometimes referred to as Panchangam (पञ्चाङ्ग), which is known also known as Panjika in Eastern India.[3]

A page from the Hindu calendar 1871-72

The ancient Hindu calendar conceptual design is also found in the Jewish calendar, but different from the Gregorian calendar.[4] Unlike the Gregorian calendar which adds additional days to the lunar month to adjust for the mismatch between twelve lunar cycles (354 lunar days)[5] and nearly 365 solar days, the Hindu calendar maintains the integrity of the lunar month, but inserts an extra full month by complex rules, once every 32–33 months, to ensure that the festivals and crop-related rituals fall in the appropriate season.[4][2]

The Hindu calendars have been in use in the Indian subcontinent since Vedic times, and remain in use by the Hindus all over the world, particularly to set Hindu festival dates. Early Buddhist communities of India adopted the ancient Vedic calendar, later Vikrami calendar and then local Buddhist calendars. Buddhist festivals continue to be scheduled according to a lunar system.[6] The Buddhist calendar and the traditional lunisolar calendars of Cambodia, Laos, Myanmar, Sri Lanka and Thailand are also based on an older version of the Hindu calendar. Similarly, the ancient Jain traditions have followed the same lunisolar system as the Hindu calendar for festivals, texts and inscriptions. However, the Buddhist and Jain timekeeping systems have attempted to use the Buddha and the Mahavira's lifetimes as their reference points.[7][8][9]

The Hindu calendar is also important to the practice of Hindu astrology and zodiac system as well as observing special appearance days of the Lord and fasting days such as Ekadasi.

Origins

Time keeping

[The current year] minus one,
multiplied by twelve,
multiplied by two,
added to the elapsed [half months of current year],
increased by two for every sixty [in the sun],
is the quantity of half-months (syzygies).

— Rigveda Jyotisha-vedanga 4
Translator: Kim Plofker[10]

The Vedic culture developed a sophisticated time keeping methodology and calendars for Vedic rituals,[11] and timekeeping as well as the nature of solar and moon movements are mentioned in Vedic texts.[12] For example, Kaushitaki Brahmana chapter 19.3 mentions the shift in the relative location of the sun towards north for 6 months, and south for 6 months.[13][14]

Time keeping was important to Vedic rituals, and Jyotisha was the Vedic era field of tracking and predicting the movements of astronomical bodies in order to keep time, in order to fix the day and time of these rituals.[15][16][17] This study was one of the six ancient Vedangas, or ancillary science connected with the Vedas – the scriptures of Vedic Sanatan Sanskriti.[15][16]

David Pingree has proposed that the field of timekeeping in Jyotisha may have been "derived from Mesopotamia during the Achaemenid period",[18] but Yukio Ohashi considers this proposal as "definitely wrong".[19] Ohashi states that this Vedanga field developed from actual astronomical studies in ancient Vedic Period.[20] The texts of Vedic Jyotisha sciences were translated into the Chinese language in the 2nd and 3rd centuries CE, and the Rigvedic passages on astronomy are found in the works of Zhu Jiangyan and Zhi Qian.[21] According to Subhash Kak, the beginning of the Hindu calendar was much earlier. He cites Greek historians describing Maurya kings referring to a calendar which originated in 6676 BC known as Saptarsi calendar.[22]

The Vikrami calendar is named after king Vikramaditya and starts in 57 BCE.[23]

Texts

Dharmic (Hindu) scholars kept precise time by observing and calculating the cycles of Surya i.e. the sun, moon and the planets. These calculations about the sun appear in various astronomical texts in Sanskrit, such as the 5th-century Aryabhatiya by Aryabhata, the 6th-century Romaka by Latadeva and Panca Siddhantika by Varahamihira, the 7th-century Khandakhadyaka by Brahmagupta and the 8th-century Sisyadhivrddida by Lalla.[24] These texts present Surya and various planets and estimate the characteristics of the respective planetary motion.[24] Other texts such as Surya Siddhanta dated to have been completed sometime between the 5th century and 10th century present their chapters on various deified planets with stories behind them.[24]

The manuscripts of these texts exist in slightly different versions. They present Surya, planet-based calculations and Surya's relative motion to earth. These vary in their data, suggesting that the text were open and revised over their lives.[25][26][27] For example, the 1st millennium CE Sanathana Dharma (Hindu) scholars calculated the sidereal length of a year as follows, from their astronomical studies, with slightly different results:[28]

Smskrth (Sanskrit) texts: How many days in a year?

Hindu text	Estimated length of the sidereal year[28]
Surya Siddhanta	365 days, 6 hours, 12 minutes, 36.56 seconds
Paulica Siddhanta	365 days, 6 hours, 12 minutes, 36 seconds
Paracara Siddhanta	365 days, 6 hours, 12 minutes, 31.50 seconds
Arya Siddhanta	365 days, 6 hours, 12 minutes, 30.84 seconds
Laghu Arya Siddhanta	365 days, 6 hours, 12 minutes, 30 seconds
Siddhanta Shiromani	365 days, 6 hours, 12 minutes, 9 seconds

The Hindu texts used the lunar cycle for setting months and days, but the solar cycle to set the complete year. This system is similar to the Jewish and Babylonian ancient calendars, creating the same challenge of accounting for the mismatch between the nearly 354 lunar days in twelve months, versus nearly 365 solar days in a year.[4][29] They tracked the solar year by observing the entrance and departure of Surya (sun, at sunrise and sunset) in the constellation formed by stars in the sky, which they divided into 12 intervals of 30 degrees each.[30] Like other ancient human cultures, Hindus innovated a number of systems of which intercalary months became most used, that is adding another month every 32.5 months on average.[29] As their calendar keeping and astronomical observations became more sophisticated, the Hindu calendar became more sophisticated with complex rules and greater accuracy.[29][31][30]

According to Scott Montgomery, the Siddhanta tradition at the foundation of Hindu calendars predate the Christian era, once had 18 texts of which only 5 have survived into the modern era.[29] These texts provide specific information and formulae on motions of sun, moon and planets, to predict their future relative positions, equinoxes, rise and set, with corrections for prograde, retrograde motions, as well as parallax. These ancient scholars attempted to calculate their time to the accuracy of a truti (29.63 microseconds). In their pursuit of accurate tracking of relative movements of celestial bodies for their calendar, they had computed the mean diameter of the earth, which was very close to the actual 12,742 km (7,918 mi).[29][30]

Hindu calendars were refined during the Gupta era astronomy by Āryabhaṭa and Varāhamihira in the 5th to 6th century. These, in turn, were based in the astronomical tradition of Vedāṅga Jyotiṣa, which in the preceding centuries had been standardised in a number of (non-extant) works known as Sūrya Siddhānta. Regional diversification took place in the medieval period. The astronomical foundations were further developed in the medieval period, notably by Bhāskara II (12th century).

Astrology

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.[16][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.[17] Later medieval era texts such as the Yavana-jataka and the Siddhanta texts are more astrology-related.[36]

Balinese Hindu calendar

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]

Year: Samvat

Samvat refers to era of the several Hindu calendar systems in Nepal and India, in a manner that the consecutive years 1 BC and AD 1 mark the Christian era and the BC/AD system. There are several samvat found in historic Buddhist, Hindu and Jaina texts and epigraphy, of which three are most significant: Vikrama era, Old Shaka era and Shaka era of 78 AD.[38]

The Hindu calendar saka samvat system is found in Indonesian inscriptions, such as the above dated to 611 CE.[39][40]

• Vikram Samvat: A northern India almanac which started in 57 BCE, and is also called the Vikrama Era. It is related to the Bikrami calendar, and is linked to Vikramaditya. This system is common in epigraphic evidence from northern, western, central and eastern Indian subcontinent, particularly after the early centuries of the 1st millennium CE.[38]
• Shaka Samvat: There are two Shaka era system in scholarly use, one is called Old Shaka Era, whose epoch is uncertain, probably sometime in the 1st millennium BCE because ancient Buddhist, Jaina and Hindu inscriptions and texts use it. However, the starting point of Old Shaka Era is a subject of dispute among scholars. The second system is called Saka Era of 78 AD, or simply Saka Era, a system that is common in epigraphic evidence from southern India.[38]
• Saka era of Southeast Asia: The Hindu calendar system in Indonesia is attributed to the legend of Hindus arriving with a sage Aji Saka in the 1st century Java, in the March of 78 CE.[41][42] Numerous ancient and medieval era texts and inscriptions found in Indonesian islands use this reference year.[43][44] In mainland southeast Asia, the earliest verifiable use of Hindu Saka methodology in inscriptions is marked Saka 533 in Ankor Borei, which corresponds to 611 CE, while in the Indonesian islands, the Kedukan Bukti inscription in Sumatra, marked to Saka 605 (683 CE) is one of the earliest known.[44] However, these inscriptions set the floruit, and the Hindu calendaring methodology likely existed in southeast Asia before these dates to be used in important monuments. Further, the Hindu calendar system remained popular among the Hindus through about the 15th century, and thereafter in Bali Indonesia.[44]
• Indian national calendar (modern): combined many Hindu calendars into one official standardized one, but old ones remain in use.[45]

Months

Amanta and Purnima systems

Two traditions have been followed in the Indian subcontinent with respect to lunar months: Amanta tradition which ends the lunar month on no moon day, while Purnimanta tradition which ends it on full moon day.[46]

The Amanta (Amavasyanta, Mukhyamana) tradition is followed by all Indian states that have a peninsular coastline (except Odisha), as well as Assam and Tripura. The states are Gujarat, Maharashtra, Goa, Karnataka, Kerala, Tamilnadu, Andhra Pradesh, Telangana, and West Bengal. Odisha and all other states follow the Purnimanta (Gaunamana) tradition.

Purnimanta tradition was being followed in the Vedic era. It was replaced with Amanta system and in use as the Hindu calendar system prior to 1st century BCE, but the Purnimanta tradition was restarted in 57 BCE by Vikramaditya who wanted to return to the Vedic roots.[46] 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.[46][47]

Paksha

A 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.[48] 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.[49]

A combination of the Paksha system, and the two traditions of Amanta and Purnimanta systems, has led to alternate ways of dating any festival or event in the historic Hindu, Buddhist or Jain literature, and contemporary regional literature or festival calendars. For example, the Hindu festival of colours called Holi falls on the first day (full moon) of Chaitra lunar month's dark fortnight in the Purnimanta system, while the same exact day for Holi is expressed in Amanta system as the Purnima (full moon) lunar day of Phalguna.[31] Both time measuring and dating systems are equivalent ways of meaning the same thing, 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]

Solar month names

There are 12 months in the Vedic lunar calendar (Sanskrit: मासाः). If the transits of the Sun through various constellations (Rāśi) are used, then we get solar months, which do not shift with reference to the Gregorian calendar. In practice, solar months are mostly referred as Rāśi (not months). The solar months (Rāśi) along with the approximate correspondence to Hindu seasons and Gregorian months are:[30]

Rāśi	Vikrami lunar months[31]	Sidereal signs	Gregorian months[31]	Ṛtu (season)	Ṛtu in Devanagari script	Bengali name for Ṛtu	Gujarati name for Ṛtu	Kannada name for Ṛtu	Kashmiri name for Ṛtu	Malayalam name for Ṛtu	Odia name for Ṛtu	Tamil name for Ṛtu	Telugu name for Ṛtu	Tibetan name for Ṛtu	Kalachakra tantra Tibetan-name for Ṛtu
Mīna Mesh	Chaitra Vaishakha	♓ ♈	Mid Mar– Mid May	Vasanta (Spring)	वसन्त	বসন্ত (Bôsôntô)	વસંત ઋતુ (Vasaṃta r̥tu)	ವಸಂತ ಋತು (Vasaṃta Ṛtu)	سونٛتھ [sõ:tʰ]	വസന്തം‌ (Vasaṃtam)	ବସନ୍ତ (Basanta)	பின்பனி (pinpani)	వసంత ఋతువు (Vasaṃta Ṛtuvu)	དཔྱིད་ར་བ་དང་དཔྱིད་བར་མ (shid rawa, thang, shid warma)	དཔྱིད་ཀ (shid ka)
Vṛṣabha Mithuna	Jyeshtha Aashadh	♉ ♊	Mid May– Mid July	Grīṣma (Summer)	ग्रीष्म	গ্রীষ্ম (Grishsho)	ગ્રીષ્મ ઋતુ (Grīṣma r̥tu)	ಗ್ರೀಷ್ಮ ಋತು (Grīṣma Ṛtu)	گرٛێشِم [greʃim]	ഗ്രീഷ്മം (Grīṣmam)	ଗ୍ରୀଷ୍ମ (Grīṣma)	இளவேனில் (ilavenil)	గ్రీష్మ ఋతువు (Grīṣma Ṛtuvu)	དཔྱིད་ཐ་མ་དང་དབྱར་ར་བ། (shid dama, thang, yar rawa)	སོ་ག(soga)
Karkaṭa Siṃha	Shraavana Bhadrapad	♋ ♌	Mid July– Mid Sep	Varṣā (Monsoon)	वर्षा	বর্ষা (Bôrsha)	વર્ષા ઋતુ (Varṣa r̥tu)	ವರ್ಷ ಋತು (Varṣa Ṛtu)	ؤہراتھ [wəhraːtʰ]	വര്‍ഷം‌ (Varṣām)	ବର୍ଷା (Barṣā)	முதுவேனில் (mudhuvenil)	వర్ష ఋతువు (Varṣa Ṛtuvu)	དབྱར་བར་མ་དང་དབྱར་ཐ་མ (yarwarma, thang, yardama)	དབྱར་ག (yarka)
Kanyā Tulā	Ashvin Kaartik	♍ ♎	Mid Sep– Mid Nov	Śarad (Autumn)	शरद्	শরৎ(Shôrôt)	શરદ ઋતુ (Śarad r̥tu)	ಶರದೃತು (Śaradṛtu)	ہَرُد [harud]	ശരത്‌ (Śarat)	ଶରତ (Śarata)	கார் (kaar)	శరదృతువు (Śaradṛtuvu)	སྟོན་ར་བ་དང་སྟོན་བར་མ (ston rawa, thang, ston warma)	སྟོན་ཁ (stonka)
Vṛścik‌‌‌a Dhanu	Agrahayana (Margashirsha) Poush	♏ ♐	Mid Nov– Mid Jan	Hemanta (Pre-Winter)	हेमन्त	হেমন্ত (Hemôntô)	હેમંત ઋતુ (Hēmaṃta r̥tu)	ಹೇಮಂತ ಋತು (Hēmaṃta Ṛtu)	وَنٛدٕ [wandɨ]	ഹേമന്തം‌ (Hemantam)	ହେମନ୍ତ (Hemanta)	குளிர் (kulir)	హేమంత ఋతువు (Hēmaṃta Ṛtuvu)	སྟོན་ཐ་མ་དང་དགུན་ར་བ (ston da ma, thang, dgun rawa)	དགུན་སྟོད (dgun stod)
Makara Kumbha	Magha Phalgun	♑ ♒	Mid Jan– Mid March	Śiśira (Winter)	शिशिर	শীত (Śeet)	શિશિર ઋતુ (Śiśira r̥tu)	ಶಿಶಿರ ಋತು (Śiśira Ṛtu)	شِشُر [ʃiʃur] or شِشِر [ʃiʃir]	ശിശിരം‌ (Śiśiram)	ଶୀତ/ଶିଶିର (Śīta/Śiśira)	முன்பனி (munpani)	శిశిర ఋతువు (Śiśira Ṛtuvu)	དགུན་བར་མ་དང་དགུན་ཐ་མ (dgun warma, thang, dgun dama)	དགུན་སྨད (dgun smad)

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

Lunar months and approximate correspondence

The names of the Hindu months vary by region. Despite the significant differences between Indo-European languages and Dravidian languages, 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]

The Tamil lunar month names are forward shifted by a month compared to Vikrami month names, in part because Tamil calendar integrates greater emphasis for the solar cycle in a manner similar to the neighboring Kerala region and it follows the Amanta system for lunar months. This is in contrast to Vikrami calendar which keeps the Purnimanta system and emphasizes the lunar cycle.[50] A few major calendars are summarized below:

Calendar month names in different Hindu calendars[1]

#	Vikrami (lunar)[31]	Vikrami (solar)	Hindi	Assamese	Bengali	Kannada/Telugu	Kashmiri	Malayalam (solar)	Odia	Punjabi	Sindhi	Tamil	Tulu (solar)	Tibetan (lunar)	Gregorian
1	Chaitra	Mina	चैत्र	চৈত (Sót)	চৈত্র (Choitrô)	ಚೈತ್ರ (Chaitra)	ژِتھٕر [t͡sitʰɨr]	Minam	ଚୈତ୍ର (Chaitra)	ਚੇਤ (Chēt)	چيٽُ‎ (Chēṭu)	Chithirai	Suggi	ནག་པ་ཟླ་བ	March–April
2	Vaisākha	Mēsha	वैशाख	বহাগ (Böhag)	বৈশাখ (Boiśākh)	ವೈಶಾಖ (Vaisākha)	وَہؠکھ [wahʲakʰ] or بیساکھ [beːsaːkʰ]	Medam	ବୈଶାଖ (Baiśākha)	ਵਸਾਖ (Vasākh)	ويساکُ‎ (Vēsākhu) or وِهاءُ‎ (Vihāu)	Vaigasi	Paggu	ས་ག་ཟླ་བ	April–May
3	Jyeshta	Vrisha	ज्येष्ठ	জেঠ (Zeth)	জ্য়ৈষ্ঠ (Jyoisthô)	ಜ್ಯೇಷ್ಠ (Jyeshta)	زیٹھ [zeːʈʰ]	Edavam	ଜ୍ୟେଷ୍ଠ (Jyeṣṭha)	ਜੇਠ (Jēṭh)	ڄيٺُ (Jēṭhu)	Aani	Bēsha	སྣྲོན་ཟླ་བ	May–June
4	Āshāda	Mithuna	आषाढ़	আহাৰ (Ahar)	আষাঢ় (Āsādh)	ಆಷಾಢ (Āshāda)	ہار [haːr]	Mithunam	ଆଷାଢ଼ (Āsādha)	ਹਾੜ੍ਹ (Hāṛh)	آکاڙُ‎ (Ākhāṛu) or آهاڙُ‎ (Āhāṛu)	Aadi	Kārtel	ཆུ་སྟོད་ཟླ་བ	June–July
5	Shraavana	Karka	श्रावण	শাওণ (Xaün)	শ্রাবণ (Śrābôṇ)	ಶ್ರಾವಣ (Shrāvana)	شرٛاوُن [ʃraːwun]	Karkadakam	ଶ୍ରାବଣ (Śrābaṇa)	ਸਾਓਣ (Sāoṇ)	سانوَڻُ (Sānvaṇu)	Aavani	Aaṭi	གྲོ་བཞིན་ཟླ་བ	July–August
6	Bhādra	Singa	भाद्रपद	ভাদ (Bhado)	ভাদ্র (Bhādrô)	ಭಾದ್ರಪದ (Bhādrapada)	بٲدٕرپؠتھ [bəːdɨrpʲatʰ] or بٲدرؠتھ [bəːdrʲatʰ]	Chingam	ଭାଦ୍ରବ (Bhādraba)	ਭਾਦੋਂ (Bhādōn) or ਭਾਦਰੋਂ (Bhādrōn)	بَڊو‎ (Baḍo) or بَڊرو (Baḍro)	Purattasi	Sona	ཁྲིམས་སྟོད་ཟླ་བ	August–September
7	Ashwina	Kanya	आश्विन	আহিন (Ahin)	আশ্বিন (Āśhshin)	ಆಶ್ವಯುಜ (Āswayuja)	ٲشِد [əːʃid]	Kanni	ଆଶ୍ୱିନ (Āświna)	ਅੱਸੂ (Assū)	اَسُو (Asū)	Aippasi	Kanya/Nirnāl	ཐ་སྐར་ཟླ་བ	September–October
8	Kartika	Tula	कार्तिक	কাতি (Kati)	কার্তিক (Kārtik)	ಕಾರ್ತೀಕ (Kārtika)	کارتِکھ [kaːrtikʰ]	Tulam	କାର୍ତ୍ତିକ (Kārttika)	ਕੱਤਕ (Kattak)	ڪَتِي (Katī)	Karthigai	Bontel	སྨིན་དྲུག་ཟླ་བ	October–November
9	Mārgasirsa (Agrahayana)	Vrischika	मार्गशीर्ष	আঘোণ (Aghün)	অগ্রহায়ণ (Ôgrôhāyôn)	ಮಾರ್ಗಶಿರ (Mārgasira)	مَنٛجہۆر [mand͡ʒhor] or مۄنٛجہِ ہور [mɔnd͡ʒihoːr] or مَگَر [magar]	Vrischikam	ମାର୍ଗଶିର (Mārgaśira)	ਮੱਘਰ (Magghar)	ناهرِي (Nāhrī) or مَنگهِرُ‎ (Manghiru)	Margazhi	Jārde	མགོ་ཟླ་བ	November–December
10	Pausha	Dhanus	पौष	পোহ (Puh)	পৌষ (Poush)	ಪುಷ್ಯ (Pushya)	پوہ [poːh] or پۄہ [pɔh]	Dhanu	ପୌଷ (Pauṣa)	ਪੋਹ (Poh)	پوهُه (Pohu)	Thai	Perarde	རྒྱལ་ཟླ་བ	December–January
11	Māgha	Makara	माघ	মাঘ (Magh)	মাঘ (Māgh)	ಮಾಘ (Magha)	ماگ [maːg]	Makaram	ମାଘ (Māgha)	ਮਾਘ (Māgh)	مانگھُه (Mānghu)	Maasi	Puyintel	མཆུ་ཟླ་བ	January–February
12	Phālguna	Kumbha	फाल्गुन	ফাগুন (Phagun)	ফাল্গুন (Phālgun)	ಫಾಲ್ಗುಣ (Phalguna)	پھاگُن [pʰaːgun]	Kumbham	ଫାଲ୍ଗୁନ (Phālguna)	ਫੱਗਣ (Phaggaṇ)	ڦَڳُڻُ (Phaguṇu)	Panguni	Māyi	དབོ་ཟླ་བ	February–March

Corrections between lunar and solar months

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. 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]

Rare corrections

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]

Day

Just like months, the Hindu calendar has two measures of a day, one based on the lunar movement and the other on solar. The solar day or civil day, called divasa ( दिवस), has been what most Hindus traditionally use, is easy and empirical to observe, by poor and rich, with or without a clock, and it is defined as the period from one sunrise to another. The lunar day is called tithi (तिथि), and this is based on complicated measures of lunar movement. A lunar day or tithi may, for example, begin in the middle of an afternoon and end next afternoon.[54] Both these days do not directly correspond to a mathematical measure for a day such as equal 24 hours of a solar year, a fact that the Hindu calendar scholars knew, but the system of divasa was convenient for the general population. The tithi have been the basis for timing rituals and festivals, while divasa for everyday use. The Hindu calendars adjust the mismatch in divasa and tithi, using a methodology similar to the solar and lunar months.[55]

A Tithi is technically defined in Vedic texts, states John E. Cort, as "the time required by the combined motions of the sun and moon to increase (in a bright fortnight) or decrease (in a dark fortnight) their relative distance by twelve degrees of the zodiac.[56] These motions are measured using a fixed map of celestial zodiac as reference, and given the elliptical orbits, a duration of a tithi varies between 21.5 and 26 hours, states Cort.[56] However, in the Indian tradition, the general population's practice has been to treat a tithi as a solar day between one sunrise to next.[56]

A lunar month has 30 tithi. The technical standard makes each tithi contain different number of hours, but helps the overall integrity of the calendar. Given the variation in the length of a solar day with seasons, and moon's relative movements, the start and end time for tithi varies over the seasons and over the years, and the tithi adjusted to sync with divasa periodically with intercalation.[57]

Weekday/Vāsara

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]

Names of the weekdays in regional languages

No.	Sanskrit[59][60]	Latin weekday	Celestial object	Assamese	Bengali	Bhojpuri	Gujarati	Hindi	Kannada	Kashmiri	Malayalam	Marathi	Nepali	Odia	Punjabi (Hindus and Sikhs)[note 1]	Rohingya	Sindhi	Sylheti	Tamil	Telugu	Urdu
1	Ravivāsara रविवासर or Aditya vāsara आदित्य वासर	Sunday/dies Solis	Ravi, Aditya = Sun	Dêûbār/Rôbibār দেওবাৰ/ৰবিবাৰ	Rôbibār রবিবার	Aitwār अतवार	Ravivār રવિવાર	Ravivār रविवार	Bhānuvāra ಭಾನುವಾರ	[aːtʰwaːr] آتھوار	Njaayar ഞായർ	Ravivāra रविवार	Aaitabar आइतवार	Rôbibārô ରବିବାର	Aitvār ਐਤਵਾਰ	Rooibar	Ācharu آچَرُ or Ārtvāru آرتوارُ‎	Rôibbār ꠞꠂꠛ꠆ꠛꠣꠞ	Nyayiru ஞாயிறு	Ādivāraṁ ఆదివారం	Itwaar اتوار
2	Somavāsara सोमवासर	Monday/dies Lunae	Soma (deity), Chandra = Moon	Xûmbār সোমবাৰ	Śombār সোমবার	Somār सोमार	Sōmavār સોમવાર	Somavār सोमवार	Sōmavāra ಸೋಮವಾರ	[t͡səndrɨwaːr] ژٔنٛدرٕوار	Thinkal തിങ്കൾ	Somavāra सोमवार	Sombar सोमवार	Somôbārô ସୋମବାର	Somavār ਸੋਮਵਾਰ	Cómbar	Sūmaru سُومَرُ	Śombār ꠡꠝ꠆ꠛꠣꠞ	Thingal திங்கள்	Sōmavāraṁ సోమవారం	Sōmvār سوموار or Pīr پیر
3	Maṅgalavāsara मङ्गलवासर or Bhaumavasara भौम वासर	Tuesday/dies Martis	Maṅgala = Mars	Môṅôlbār/Môṅgôlbār মঙলবাৰ/মঙ্গলবাৰ	Môṅgôlbār মঙ্গলবার	Mangar मंगर	Maṅgaḷavār મંગળવાર	Maṅgalavār मंगलवार	Maṁgaḷavāra ಮಂಗಳವಾರ	[boːmwaːr] بوموار or [bɔ̃waːr] بۄنٛوار	Chovva ചൊവ്വ	Maṅgaḷavāra मंगळवार	Mangalbar मङ्गलवार	Môṅgôḷôbārô ମଙ୍ଗଳବାର	Maṅgalavār ਮੰਗਲਵਾਰ	Mongolbar	Mangalu مَنگلُ or Angāro اَنڱارو	Môṅgôlbār ꠝꠋꠉꠟ꠆ꠛꠣꠞ	Chevvai செவ்வாய்	Maṁgaḷavāraṁ మంగళవారం	Mangal منگل
4	Budhavāsara बुधवासर or Saumya vasara सौम्य वासर	Wednesday/dies Mercurii	Budha = Mercury	Budhbār বুধবাৰ	Budhbār বুধবার	Buddh बुध	Budhavār બુધવાર	Budhavāra बुधवार	Budhavāra ಬುಧವಾರ	[bɔdwaːr] بۄد وار	Budhan ബുധൻ	Budhavāra बुधवार	Budhabar बुधवार	Budhôbārô ବୁଧବାର	Buddhavār ਬੁੱਧਵਾਰ	Buidbar	Budharu ٻُڌَرُ or Arbā اَربع	Budbār ꠛꠥꠗ꠆ꠛꠣꠞ	Budhan புதன்	Budhavāraṁ బుధవారం	Budh بدھ
5	Guruvāsara गुरुवासर or Brhaspati vāsara बृहस्पतिवासर	Thursday/dies Iovis/Jupiter	Deva-Guru Bṛhaspati = Jupiter	Brihôspôtibār বৃহস্পতিবাৰ	Brihôśpôtibār বৃহস্পতিবার	Bi'phey बियफे	Guruvār ગુરુવાર	Guruvār गुरुवार or Brihaspativāra बृहस्पतिवार	Guruvāra ಗುರುವಾರ	[braswaːr] برَٛسوار or [brʲaswaːr] برٛؠسوار	Vyaazham വ്യാഴം	Guruvāra गुरुवार	Bihibar बिहीवार	Gurubārô ଗୁରୁବାର	Vīravār ਵੀਰਵਾਰ	Bicíbbar	Vispati وِسپَتِ‎ or Khamīsa خَميِسَ‎	Birôiśôtbār ꠛꠤ?ꠛꠣꠞ	Vyazhan வியாழன்	Guruvāraṁ, Br̥haspativāraṁ గురువారం, బృహస్పతివారం, లక్ష్మీవారం	Jum'erāt جمعرات
6	Śukravāsara शुक्रवासर	Friday/dies Veneris	Śukra = Venus	Xukurbār/Xukrôbār শুকুৰবাৰ/শুক্রবাৰ	Śukrôbār শুক্রবার	Sukkar सुक्कर	Śukravār શુક્રવાર	Śukravār शुक्रवार	Śukravāra ಶುಕ್ರವಾರ	[ʃokurwaːr] شۆکُروار or [jumaːh] جُمعہ	Velli വെള്ളി	Śukravāra शुक्रवार	Sukrabar शुक्रवार	Śukrôbārô ଶୁକ୍ରବାର	Śukkaravār ਸ਼ੁੱਕਰਵਾਰ	Cúkkurbar	Śukru شُڪرُ or Jum'o جُمعو	Śukkurbār ꠡꠥꠇ꠆ꠇꠥꠞ꠆ꠛꠣꠞ/ꠎꠥꠝ꠆ꠝꠣꠛꠣꠞ	Velli வெள்ளி	Śukravāraṁ శుక్రవారం	Śukarvār شکروار or Juma'a جمع
7	Śanivāsara शनिवासर	Saturday/dies Saturnis	Śani = Saturn	Xônibār শনিবাৰ	Śônibār শনিবার	Sanichchar सनिच्चर	Śanivār શનિવાર	Śanivār शनिवार	Śanivāra ಶನಿವಾರ	[baʈɨwaːr] بَٹہٕ وار	Shani ശനി	Śanivāra शनिवार	Sanibar शनिवार	Śônibārô ଶନିବାର	Śanīvār ਸ਼ਨੀਵਾਰ or Śaniccharavār ਸ਼ਨਿੱਚਰਵਾਰ	Cónibar	Chancharu ڇَنڇَرُ‎ or Śanscharu شَنسچَرُ	Śônibār ꠡꠘꠤꠛꠣꠞ	Shani சனி	Śanivāraṁ శనివారం	Śanīchar سنیچر or Haftah ہفتہ

1. Punjabi Muslims use Urdu/Arabic words for Friday / Saturday etc.[61]

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.

Five limbs of time

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.

Yoga

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:

1. Viṣkambha
2. Prīti
3. Āyuśmān
4. Saubhāgya
5. Śobhana
6. Atigaṇḍa
7. Sukarma
8. Dhrti
9. Śūla
10. Gaṇḍa
11. Vṛddhi
12. Dhruva
13. Vyāghatā
14. Harṣaṇa
15. Vajra
16. Siddhi
17. Vyatipāta
18. Variyas
19. Parigha
20. Śiva
21. Siddha
22. Sādhya
23. Śubha
24. Śukla
25. Brahma
26. Māhendra
27. Vaidhṛti

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

Karaṇa

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

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 )

Nakshatra

Nakshatras are divisions of ecliptic, each 13° 20', starting from 0° Aries. The purnima of each month is synchronised with a nakshatra.

Festival calendar: solar and lunar dates

Many holidays in the Hindu, Buddhist and Jaina traditions are based on the lunar cycles in the lunisolar timekeeping with foundations in the Hindu calendar system. A few holidays, however, are based on the solar cycle, such as the Vaisakhi, Pongal and those associated with Sankranti.[63] The dates of the lunar cycle based festivals vary significantly on the Gregorian calendar and at times by several weeks.The solar cycle based ancient Hindu festivals almost always fall on the same Gregorian date every year and if they vary in an exceptional year, it is by one day.[64]

Regional variants

The Hindu Calendar Reform Committee, appointed in 1952, identified more than thirty well-developed calendars, in use across different parts of India.

Variants include the lunar emphasizing Vikrama, the Shalivahana calendars, as well as the solar emphasizing Tamil calendar and Malayalam calendar. The two calendars most widely used today are the Vikrama calendar, which is in followed in western and northern India and Nepal, the Shalivahana Shaka calendar which is followed in the Deccan region of India (Comprising present day Indian states of Telangana, Andhra Pradesh, Karnataka, Maharashtra, and Goa).[65]

Lunar

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

• Vikram Samvat- North, West and Central India, Nepal, Sikkim
• Shalivahana era calendar- Maharashtra, Goa, Karnataka, Andhra Pradesh, Telangana
• Gujarati calendar- Gujarat
• Kashmiri calendar (Saptarshi Era)- Kashmiri Pandits
• Nepal Sambat- Newaris in Nepal, Sikkim
• Meitei calendar- Manipur

Solar

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
• Punjabi calendar- Punjab, Haryana

Other related calendars across India and Asia

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

See also

• Hindu astrology
• Hindu units of time
• Hindu units of measurement
• List of Hindu festivals
• Panchangam
• Panjika
• Ancient Vedic units of measurement
• Buddhist calendar
• Pambu Panchangam
• Kollam era
• List of Hindu Empires and Dynasties
• Ekadashi

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Bibliography

• Kim Plofker (2009). Mathematics in India. Princeton University Press. ISBN 0-691-12067-6.
• Pingree, David (1973). "The Mesopotamian Origin of Early Indian Mathematical Astronomy". Journal for the History of Astronomy. SAGE. 4 (1). Bibcode:1973JHA.....4....1P. doi:10.1177/002182867300400102.
• 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).
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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
• S. Balachandra Rao, Indian Astronomy: An Introduction, Universities Press, Hyderabad, 2000.
• Rai Bahadur Pandit Gaurishankar Hirachand Ojha, The Paleography of India, 2 ed., Ajmer, 1918, reprinted Manshuram Manoharlal publishers, 1993.

External links

• Kyoto University Gregorian – Saka – Vikrami Calendar Converter Tool, M. YANO and M. FUSHIMI
• Converter: Gregorian and 1957 Normalized Indian Calendar, Shalivahana Hindu calendar, United Kingdom
• Hindu Calendar of Nepal The Official Hindu Calendar of Nepal
• Hindu Odia Calendar The most followed Hindu Odia Calendar of Odisha, India
• Hindu Calendar 2020 Fasting Dates & Festivals for New Delhi, India
• Accurate Hindu Calendar/Drik Panchang
• Today Marathi Calendar current year
• Indian Hindu Calendar 2020 in Hindi