Hindu calendar

The Hindu calendar is of two types:

the solar calendar or the saura māna
the lunisolar calendar or the chāndra māna

Both are described in this article.

Basic structure

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. We shall first describe the day, then the months and year of the solar calendar, and then the months and year of the lunisolar calendar. Then we shall speak about 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:

the tithi active at sunrise
the weekday
the nakshatra in which the moon resides at sunrise
the yoga active at sunrise
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 angular distance (measured anticlockwise) between the sun and moon as measured from the earth can vary between 0° and 360°. This is divided into 30 parts. Each part ends at 12°, 24° etc. The circle ends at 360°. The time spent by the moon in each of this parts (i.e. the time taken for the angular distance to change by 12°) is called one tithi.

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.

Weekday

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

Ravi vāsara
Soma vāsara
Mangala vāsara
Budha vāsara
Guru vāsara
Shukra vāsara
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".

Nakshatra

The ecliptic (circle on the sky in which the sun, moon and planets seem to move) is divided into 27 nakshatra-s, which are variously called lunar houses or asterisms. 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 in parentheses 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.

Ashvinī	β and γ Arietis
Bharanī	35, 39, and 41 Arietis
Krittikā	Pleiades
Rohinī	Aldebaran
Mrighashīrsha	λ, φ Orionis
Ārdrā	Betelgeuse
Punarvasu	Castor and Pollux
Pushya	γ, δ and θ Cancri
Āshleshā	δ, ε, η, ρ, and σ Hydrae
Maghā	Regulus
Pūrva Phalgunī	δ and θ Leonis
Uttara Phalgunī	Denebola
Hasta	α to ε Corvi
Chitrā	Spica
Svātī	Arcturus
Vishākhā	α, β, γ and ι Librae
Anūrādha	β, δ and π Scorpionis
Jyeshtha	α, σ, and τ Scorpionis
Mūla	ε, ζ, η, θ, ι, κ, λ, μ and ν Scorpionis
Pūrva Ashādhā	δ and ε Sagittarī
Uttara Ashādhā	ζ and σ Sagittarī
Shravana	α, β and γ Aquilae
Shravishthā	α to δ Delphinis
Shatabhishaj	γ Aquarī
Pūrva Bhādrapada	α and β Pegasi
Uttara Bhādrapada	γ Pegasi and α Andromedae
Revatī	ζ Piscium

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. Now 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°.) Now 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.) Now these parts are called the yoga-s. They are labeled:

Vishkambha
Prīti
Āyushmān
Saubhāgya
Shobhana
Atiganda
Sukarman
Dhriti
Shūla
Ganda
Vriddhi
Dhruva
Vyāghāta
Harshana
Vajra
Siddhi
Vyatīpāta
Varīyas
Parigha
Shiva
Siddha
Sādhya
Shubha
Shukla
Brāhma
Aindra
Vaidhriti

Again, minor variations many 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. Since the tithi-s are 30 in number, one would expect there to be 60 karana-s. But there are only eleven. There are four "fixed" karana-s and seven "repeating" karana-s. The four "fixed" karana-s are:

Kimstughna
Shakuni
Nāga
Chatushpād

The seven "repeating" karana-s are:

Bava
Bālava
Kaulava
Taitila
Gara
Vanija
Vishti

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".

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. They are:

Mesha
Vrishabha
Mithuna
Kataka
Simha
Kanyā
Tulā
Vrishchika
Dhanus
Makara
Kumbha
Mīna

These are the Sanskrit equivalents of the zodiac - Aries etc.

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 is because the path of the earth around the sun is an ellipse. 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. The days are not labeled separately from 1 as in the solar calendar, but the tithi is their only label. When two successive days have the same tithi, 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".

The lunar month names are:

Chaitra
Vaishākha
Jyaishtha
Āshādha
Shrāvana
Bhādrapada
Āshvayuja
Kārtika
Mārgashīrsha
Pausha
Māgha
Phālguna

Naming lunar months

The naming of the lunar months is somewhat complex. 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 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.

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 or "original". [Note that an adhika month is the first of two whereas an adhika tithi is the second of two.]

An adhika māsa (month) occurs once every two or three years.

Lost Months

Now if the sun transits into two rāshi-s within a lunar month, then the lunar month will be labeled by the first transit and will take the epithet kshaya or "loss". Actually, the month "lost" is the month which would have been labeled by the second transit. For example, if the sun transits into Mesha and Vrishabha in a lunar month, then it will be called Chaitra kshaya. There will be no month labeled 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 kshaya. Feb-13 onwards was (adhika) Phālguna and not Māgha. Māgha was "lost" that year.

Special Case: If there is no solar transit in a 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 its first transit (as usual) and take the epithet kshaya.

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 kshaya. Dec-06 onwards was Pausha, not Mārgashīrsha.

Handling of 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, 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.

A festival which is to be observed on a month that was lost will be observed on the corresponding "previous" i.e. kshaya month. For example, the festival of Mahāshivarātri which is to be observed on the fourteenth tithi of the dark fortnight of Māgha was, in 1983 CE, observed on the corresponding tithi of Pausha kshaya, since in that year, Māgha was lost, as we mentioned above.

Year of the lunisolar calendar

The new year day is the first day of the month of Chaitra. In case of adhika Chaitra or Chaitra kshaya the rules outlined above will apply.

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 and names

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. Today (as of writing this on 2005-05-18) the elapsed years in the Hindu calendar are 5106 and this is the 5107th Hindu calendar year. Note that the lunisolar calendar year will usually start earlier than the solar calendar year.

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

Prabhava
Vibhava
Shukla
Pramoda
Prajāpati
Āngirasa
Shrīmukha
Bhāva
Yuvan
Dhātri
īshvara
Bahudhānya
Pramāthin
Vikrama
Vrisha
Chitrabhānu
Svabhānu
Tārana
Pārthiva
Vyaya
Sarvajit
Sarvadhārin
Virodhin
Vikrita
Khara
Nandana
Vijaya
Jaya
Manmatha
Durmukha
Hemalambi
Vilambi
Vikārin
Shārvari
Plava
Shubhakrit
Shobhana
Krodhin
Vishvāvasu
Parābhava
Plavanga
Kīlaka
Saumya
Sādhārana
Virodhikrit
Paritāpin
Pramādin
Ānanda
Rākshasa
Pingala
Kālayukti
Siddhārthin
Raudra
Durmati
Dundubhi
Rudhirodgārin
Raktāksha
Krodhana
Kshaya

Eras

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

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 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.

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.

History

The Hindu Calendar obviously 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 Sūuuūrya Siddhānta, a text of uncertain age, though some place it at 10th century.

External links

The majority of the text above was based from the pure astronomical definitions at the Hindu Solar Calendar (http://samvit.org/calendar/astro/hsc.htm) and at the Hindu Lunar Calendar (http://samvit.org/calendar/astro/hlc.htm).
Indian Calendar at Webexhibits.org (http://www.webexhibits.org/calendars/calendar-indian.html)
Some facts on the Hindu Calendar by Pandit Sanjay Rath (http://srath.com/lectures/hinducalendar.htm)
Vedic Calendar Program (http://www.krishna.com/downloads/Software/BBT_and_ISKCON_software/index.html) (freeware) For any modern year, anywhere in the world, tells when each tithi, each naksatra, and each lunar month occurs, and the dates for various festivals (especially Gaudiya Vaishnava). Also calculates birthdays. — Useful generally only for ISKCON adherents or North Indian Vaishnava traditions.

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