The Science behind Indian (Hindu) Calendars

(R.K. Chopra, B.Tech. Mining Engg.)


With evolution of human specie there was a need to keep track of time and to forecast certain cyclic events upon which human survival depended. The change of seasons, onset of winter & melting of snow, onset of monsoon (rain) & occurrence of flood, migration of animals & fish, and cycle of crops, plants & trees, all were governed by a time cycle, which even the animals felt and were aware of; but humans in different parts of the world devised precise systems for calculating and predicting this time cycle which later evolved as different types of calendars.

Humans took help of celestial bodies, apparent motions of the sun & the moon to formulate different calendars. Counting of days based upon the phases of the moon began in Palaeolithic Era (Stone Age, 2.5 millions year ago to 10000 BC) and thus the concept of a lunar month developed. The concept of seasons also existed right from the beginning. However, with the development of civilisations and advent of script & counting system, man could know the number of days it took for recurrence of a season and that it happened due to motion of the sun (or the earth as we know now); and concept of the solar year developed. It did not take any more time to configure that roughly 12 lunar months make a solar year.

In colder countries where onset of winter & melting of snow was the single most important factor around which activity cycle of humans, animals and plants revolved, solar calendars developed. In deserts, where most of the travelling was done at night, lunar calendars came in use. People at sea shores also relied heavily on lunar cycle for fishing. In tropical countries such as India, where climate was warmer and people usually slept outside the house, gazing the moon and stars, lunisolar calendars developed. Subsequently, these were linked to stars or group of stars.

Before understanding the science behind a calendar one must understand the following astronomical facts:


  • The Moon revolves around the earth in about 27.32 days (sidereal month), i.e. if the moon is seen after this interval, it would be near the same star.
  • On every other night one would find the moon near some other group of stars. In Indian system each such star (or group) is called Nakshatra (wives of moon, in all there are 27). Nakshatra (lunar mansion) should be distinguished from Rashis (Zodiacs), which are also groups of stars but are twelve in number and basically represent twelve months of the year (solar). Naksatras may be a part of the 12 zodiacs, or may be a constellation by themselves.
  • The average time interval between two full moons (synodic or lunar month) is about 29.53 days (29 days, 12 hours, and 44 minutes). It is longer than sidereal month because the earth moving at a speed of about 1 degree per day (360 degrees in a year) around the sun would have moved about 30 degrees ahead during this period and moon with its speed of about 12 degrees per day around the earth has to travel about 2½ days extra to come into the line of the sun and the earth (full moon). For the same reason one would find the full moon in a new zodiac (30 degrees ahead) after every month. However, this time between two full moon is also not constant and ranges from about 29.27 to 29.83 days.
  • The earth takes 365.256 days (Sidereal year, 365d 6h 9min) to make one revolution around the sun. You would find same midnight sky (stars) after this interval.
  • A tropical (climatic) year (365.242 days, 365d 5h 46m) is slightly shorter than the sidereal year and is equal to the time sun takes to return to the same position in the cycle of seasons (equinoxes/sankrantis, which are related inclination of sun rays falling on earth). This minute difference occurs because like a wobbling top, the orientation of the Earth’s axis is slowly but continuously changing in a cycle of approximately 25,765 years due to gravitational forces of the Sun and the Moon. That means that the position of the sun with respect to stars changes after every topical year. This is the basic cause of the anomalies between Gregorian calendar (based on tropical year) and some Hindu calendars (based on sidereal year) year, though both have a sound scientific base
  • 30 lunar dates are equal to 29.53 solar dates. One solar year has 371 lunar dates or tithes. This means a solar year would have about 12 1/3 lunar months. If the 12 Synodic (lunar) months are used to count a year, it will be almost 11 days shorter (354.367 days) than the tropical year.
  • An equinox happens each year twice when the centre of the sun can be observed to be vertically above the earth’s equator occurring around March 20 or 21 (Vernal/northward equinox) and September 22 or 23 (autumnal/southward equinox).
  • Northern (summer) solstice and southern (winter solstice) also indicate the sun’s position. The northern solstice takes place on June 20 or 21 when the sun is directly over the Tropic of Cancer in the Northern Hemisphere, and the southern solstice on December 21 or 22, when the sun is directly over the Tropic of Capricorn in the Southern Hemisphere.


As a solar year does not have exactly 12 lunar months; combining the two would requires some cumbersome calculations, and if a thumb rule is applied inaccuracy will crop in. On the other hand, with the sole use of a lunar calendar with 12 lunar months a year, dates or festivals will keep shifting into different seasons every year (advancing by about 11 days after each solar year).

The biggest advantage of lunar calendar is that it is simple and dates could be tracked even by an illiterate man in early days when no paper or printing existed. Solar calendars kept track of seasons. But remembering a date was the job of the learned men. The lunisolar calendar had the advantage of both worlds, but involved some mathematics (like the value of Pi or π, an accurate calculation need not be simple).

Earlier Roman calendar had only 10 months. September was the seventh month, October the eighth, November the ninth and December the tenth. A calendar year lasted only 304 days and winter months were simply ignored. After many reforms, came the Gregorian calendar which is the most widely used in the world today. It has an average year of 365.2425 days with an error of about one day per 3300 years with respect to the mean tropical year of 365.2422 days.

India has an ancient astronomical tradition, though it is difficult to trace its development due to the lack of systematic historical records. One has to interpret the astronomical references from the ancient literatures. Indian Astronomy existed even before 1400 BC, much earlier to the Babylonian astronomy (thrived in 5th century). Concepts of tithis (dates) and Nakshatras (star/ star-groups or asterisms) was the part of earlier Vedic Astronomy. The present Panchangs (calendars) were made later and refined by many astronomers like Arybhatta (5th Century).

Initially, the year used to have 360 days (12 months of 30 days each). Later on astronomer-priests started the practice of having an extra month (adhikamasa) of 30 days every 6th year (thus year averaged at 365 days).

When full moon month cycle was followed, the 12 lunar months made a year of about 355 days. So, after every two and half years a lunar month (of 29.53 days) was added. Thus an average year contained 366 days( i.e. one day extra). This anomaly was rectified by dropping a month after every 30th year (30 solar years @ 365.24219 days = 10957 days; 371 lunar months @ 29.53059 days = 10956 days). The concept of dropping a month was there around 3000 BC and was carried to later period. Even then a small error of 5 lunar dates (tithes) was estimated in 90 years. Therefore a special 5 year period was added with one extra date each year after 90 years.

Above is the basis of the 95-year Agnichayana vidhi as described in the 6th Kanda of Shatapatha Brahmana शतपथ ब्राह्मण (Yajurved यजुर्वेद, 1000-1400 BC). The 95-year cycle containing 5 Metonic cycles of 19 years was discovered by the Babylonians around 300 BC. Present Indian calendars do calculations by actual positions of the sun and the moon and drop-month may occur after interval of 19 to 141 years.
Presently, following main Calendars are in use in India:

Vikrama Samvat: This is also the official calendar of Nepal. It follows lunar months, and solar sidereal years. The calendar is popular in mainland India. It was started by the emperor Vikramaditya of Ujjain following his victory over the Sakas in 56 BCE. The calendar is 56.7 years (56 Years and 8 ½ Months) ahead of the Gregorian calendar.

The names of the 12 months are taken from the 12 Nakshatras around whom the moon is placed on full moon day. The month can be identified by observing the first Naksatra on the eastern horizon at sunset. To synchronize it with the solar calendar, about once every 2 ½ years an extra month is added within a year (that means one particular month is repeated twice within that year). This way the festivals are observed by lunar dates but are contained within the same season (± 15days).

Unlike in many calendar systems where thumb rules are followed (e.g. 7 extra months in a 19 year cycle or 7 embolismic months in a24-year cycle), the Indian system is based upon actual calculations of motions the sun and the moon. The12 reference points (stars) of the sun in Hindu system, now no longer coincides with the 1st day of each month of Gregorian calendar (the gap has widened over the years as they follow sidereal or tropical system). For a month to have been completed as per the Hindu calendar, sun must traverse certain reference points. The concept is very much similar to the blue moon when two full moon occurs with in a month (average Gregorian month is about 30 ½ days and the full moon occurs after every 29-30 days. If a full moon occurs on 1st or 2nd day of a month, another full moon may occur within the same month on 30th or 31st day). Similarly it may so happen that there may not be a full moon in February if full moon day happens to be, say 31st January and 1st March. Had it been such case in Hindu lunisolar calendar, we would have added an extra month in first case and dropped a month in 2nd case.

Tithis (Dates) are counted from 1 to 15 for each 15 days period. These periods are named as Krishna Paksh (Dark fortnight, waning moon, when moon rises after sunset) and Shukla Paksh (bright fortnight waxing moon when moon is visible at the sunset). Dates are calculated based upon each 12 degree of moon phase, and Full Moon and New Moon falls on 15th day of the fortnight (This slightly differs from Islamic dates when first day is when moon is visible by human eyes and full moon occurs on 14th day). However due to complex lunation of moon in actuals, a paksh may be of 13 or 14 or 16 days also.
Shaka Samvat: (traditional): It follows lunar months, solar sidereal years. It was started after the king Shalivahana’s (Saka dynasty) victory over the dynasty of king Vikramaditya. It is used with Hindu calendars, the Indian national calendar, and the Cambodian Buddhist calendar. The new year begins near the vernal equinox.




Solar Months of the Indian Religious Calendar
Sun’s LongitudeApprox. DurationApprox. Greg.Date
deg mindays
1Vaisakha23 1530.9Apr.  13
2Jyestha53 1531.3May  14
3Asadha83 1531.5June  14
4Sravana113 1531.4July  16
5Bhadrapada143 1531.0Aug. 16
6Asvina173 1530.5Sept. 16
7Kartika203 1530.0Oct. 17
8Margasirsa233 1529.6Nov. 16
9Pausa263 1529.4Dec. 15
10Magha293 1529.5Jan. 14
11Phalgura323 1529.9Feb. 12
12Caitra353 1530.3Mar. 14


Lunations are divided into 30 tithis, or lunar days. Each tithi is defined by the time required for the longitude of the Moon to increase by 12 degrees over the longitude of the Sun. Thus the length of a tithi may vary from about 20 hours to nearly 27 hours.

Shaka Samvat: (modern) solar tropical: It is the official civil calendar in use in India, used alongside the Gregorian calendar by the Government of India. The year starts on 22nd March (21st March in leap years). The calendar is 58/59 years behind Gregorian calendar.




* In a leap year, Caitra has 31 days and Caitra 1 coincides with March 21


Regional Calendars: In many regions of India regional solar calendars are followed. The New Year starts in mid April, when, according to traditional calculations, the sun returns from southern hemisphere to northern hemisphere (Vernal equinox) and Bihu (Assam), Baisakhi (Punjab) Vishu (Kerala) and Pôhela Boishakh (Bengal) are celebrated.

Earlier practice of starting the year from winter solstice (Uttarayana day) continued throughout the Vedic period but was later changed to vernal equinox.

As Indian system followes sidereal years (based on stars/zodiacs), which is slightly larger than the tropical years (based on equinoxes or solstice) the annul date of festival of winter solstice (Makara sankranti/ Pongal) has shifted by 24 days (from 21st December to 14th January). But after deliberations by learned men, it was decided that these festivals shall continue to be celebrated on traditional days i.e. by position of sun with respect to a star rather than solstice). This difference has grown to 24 days in last about 1700 years as the full cycle is of 25765 years.


Some calendars and their year with respect to Gregorian calendar year 2008 is listed below:

1.    Sri Krishna Samvat – 5234
2.    Yudhisthira Samvat – 5151
3.    Gat Kali, – 5109 (Kalyabd 5110)
4.    Saptarsi – 5083
5.    Baudh Samvat – 2583
6.    Jaina Samvat (Mahavira Nirvana) – 2535
7.    Sri Shankaracharya Samvat – 2288
8.    Vikrama Samvat – 2065
9.    Shaka Samvat/Shalivahana Samvat – 1930
10.   Bangla Samvat – 1415
11.   Kalachuri Samvat – 1760
12.   Balabhi Samvat – 1688
13.   Fali Samvat – 1419
14.   Harshand Samvat – 1401

Indian panchangs (Calendars) follow a system dividing the time cycle in multiple of 6 or 60.for example a year was divided into 12 months and 6 seasons. Each month had 30 days. Further:

1 day       =     24 Hora (hours) =     60 Ghadi (24 minutes each)

1Ghadi     =     60 Pal

1 Pal        =     60Vipal

1 Vipal     =     30Ksan         =    60Luv

The bigger times were named as follows;

1000 years           =    1 Sahasrabda

432 Sahasrabda    =    1 Yug

10000 Yug          =    1 Kalp (4.32 billion years)

Hindus follow traditional religious Lunar Calendar to celebrate their festivals. But some festivals are followed also based on position of the sun in the Zodiac. Various states of India celebrate the New Year in their own ways. And not all of these falls on the same day, e.g.:


Northen India (Vikram)Lunisolar (Chaitra Shukla 1) March-April
Nepali (Nava Varsha)(Baisakh 1) April 13 or14
Punjabi / Sikh (Nanakshahi)Baisakhi, April 13 or 14
Kerala (Vishu)April 13 or 14
Tamil Nadu (Puthandu Vazthukal)April 13 or 14
Bengali (Nôbobôrsho)Pohela Boishakh, April 14 or 15
Assami (Bohaag Bihu)Chait Sankranthi, April 14 or 15
Sindhis (Cheti-Chand)New Moon of Cheti (Chaitra) (March-April)
(also the birthday of Jhulelal, the Patron Saint of Sindhis)
Marathi (Gudi Padva)
Andhra Pradesh, Telgu (Ugadi)*First day of Chaitra, lunisolar (March-April)
Karnataka, Kannada (Ugadi)*First day of Chaitra, lunisolar (March-April)
Kashmiri (Navreh)First day of Chaitra, lunisolar (March-April)
Marwari, Gujarati, (Bestu Varas)Diwali, Karthik Shukla Pratipada (October- November)
MuslimMuharram 1 (advance about 11 days every year)
Parsi (Zoroastrian), Iranian, BahaiNowruz 20-21 March
Sikkim (Tibet Losar)Tibetan lunisolar (January February)
Sikkim (Tamang)(Sonam Lhochar)18th day of the 10th month (Magh) of the Tibetan
lunisolar calendar    (December-January)
Sikkim (Gurang) (Tamu Losar)15th day of Pusa, 30th December
Sikkim harvest (Losoong)End of 10th Month, 28-31 December

* Yug+Aadi = Yugadi

Old Roman calendar observed New Year’s Day on March 15. The January 1 was fixed as  New Year’s Day in 153 BC.

(Note: The concept of the above article was suggested by author’s father Shri D.K. Chopra, who is a scholar of Hindu Philosophy, Mythology and astrology. However, readers may have discretion regarding sources and accuracy of data. Suggestions for improvements are welcomed).

Hindu Calendar : After reading this article some requests came to make it simpler. So I have tried to explain some of the points through an analogy.

You must have heard the phrase “Once in a Blue Moon” – meaning not very often.  Actually a blue moon is nothing but a full moon (पूर्णिमा) occurring 2nd time within an English calendar month.

As the interval between 2 full moons is 29 1/2 days, if a full moon occurs on 1st or 2nd day of the month, another full moon (called blue moon) will occur around 30th or 31st. There cannot be more than 13 full moons (or less than 12) in a year. Though it may so happen that a blue moon may occur in January and also in March, but in that case February (28 days) will not have any full moon (year 2018). It is extremely rare, once in 1000 years, that a 29 days February will not have any full moon (year 1608, 2572)

The flip side of a Blue moon is a Black Moon when in a single calendar month the 2nd new moon (Amavasya) occurs.

Our Hindu calendars are mostly based on lunar phases starting from next day of a full Moon (zero) ‘Pratipada the day one’ and ending with the Full moon. Some calendar observes new moon to new moon cycle also. There are other Hindu calendars with are based on solar phases (e.g. Bangla (Bengali) and Punjabi calendars based on solar movements) which I am not discussing here.

Since in our Hindu calendar system a month is completed after on New moon and a year should have only 12 months, there is a mechanism of addressing this extra New moon month whenever it occurs.

Roughly in 3 years time we have 37 New moons (or months, to be more precise such month occurs after 28 to 36 months, i.e. once in 32 months on average) where as we should have only 36 months in 3 years going by the fact that an year can have only 12 months. So we have an in built mechanism to bring it down to 36 named months of years by not giving the additional month any new name calling it an अधिक मास Adhik Maas (Surplus Month or पुरुषोत्तम मास Purushottam Maas, as the saying goes given when the Adhik month approached Lord Visnu crying discrimination).

Usually it is solved in two parts of 15 days each (paksh), with 30 days pure month remaining in middle and each half of Adhik maas on either side. By doing so our festivals are not much off to its solar dates (unlike in Islamic calendar where within 12 years Eid falling in summer falls in winter.

Opposit of Adhik maas is क्षय मास Kshay maas (lost or deficit month), which occurs very rarely (year 1983). For an analogy, I gave you an example of a February without a full moon. In Kshay maas, the two month names are combined and festivals of both the months covered in that.

Going by the simple arithmetic, the lost month should not happen. But due to eccentric elliptical orbit (path), the earth covers a distance of 30 degrees (of a month, dividing total path of 360 degrees into 12 parts) faster with respect to Sun during winter months (29 to 30 days) than in other months (30 to 32) days). So, although Kshay Mass is rare but does occur.


If two new moons occur between two successive Sankranti dates, an Adhik Maas or Surplus Month will be generated. On the contrary if no new moon occurs in such period, a month will be lost. The lost month is combined with another month, but certainly in that year at some point of time an Adhik Maas will also be generated. It may be sacrilegious to ask for adjusting a Kshay Mass with the Aadhik Maas happening within the same year, which is based on the precise astronomical calculations, but I do have a right to keep a different opinion.


(Starting 2017 Sankranti dates are, when the sun changes a zodiac, are March-14  April, Vrishabh- 14 May, Mithuna- 14 June, Kark- 16 July, Simh- 16 August, Kanya- 16 September, Tula- 17 October, Vrischik-16 November, Dhanu- 15 December, Makar 15 January, Kumbh- 13 February, Meen- 14 March


By this way Hindu system bridges both solar and lunar calendars.


Early Roman calendars were also based on lunar cycle and month used to start after sighting of moon just as practiced in Islamic calendar now. A year had 355 days similar to our calendars and to make the calendar correspond approximately to the solar year, the Roman ruler Numa Pompilius ordered the addition of a month called Mercedinus after every 2 years.


Earth is closest to the sun (147 million km) around 3rd January and farthest (152 million km) around 3rd July. Earth speed is fastest when it is closest to sun, Just imagine a tennis ball you toss up has the highest speed when it touches the ground and slows it down when it goes up. Then why do we have winter when we are closure to sun. Because intensity of heat variance due to distance change is only about 3%. The major change is primarily based on the tilt of the earth at any point of time towards the sun as a result, in northern hemisphere we get maximum heat at around 21st June and least around 21st December.


In the astrology the planetary position in solar system with respect to earth is considered. But the time can not be repeated if you look further beyond. For example, our Solar system has a speed of 230 km/ second making one orbit of our Galaxy, the Milky Way in 225 to 250 million years = 1 cosmic year. For comparison, the earth is moving a speed of only 29.79 km/sec making one round of sun in a year. (This is different from the speed one is getting about 0.46 km/sec at the equator due to earth rotation or spin.