भीष्म उवाच कलांशास्तात् युज्यन्ते मुहूर्त्ताश्च दिनानि च अर्धमासाश्च मासाश्च नक्षत्राणि ग्र्हास्था | ऋतवश्चापि युज्यन्ते तथा संवत्सरा अपि एवं कालविभागेन कालचक्रं प्रवर्तते | तेषां कालातिरेकेण ज्योतिषां च व्यतिक्रमात् पञ्चमे पञ्चमे वर्षे द्वौ मासावुपजायतः | तेषामभ्यधिक मासाः पञ्च द्वादश च क्षपाः त्रयोदशानां वर्षणामिति मे वर्तते मतिः |
The above is an excerpt (in Bhishma’s words) from the Virārataparva (विराटपर्व) of the Hindu epic Mahābhāratam (महाभारतम्), which roughly translates to:
The wheel of time revolves with its divisions: kalas, muhurtas, days, fortnights, months, constellations, planets, seasons and years. In consequence of their fractional excesses and the deviations of the heavenly bodies, there is an increase of two months every five years. By calculating it this way, it seems to me that there would be an excess of five months and twelve days in thirteen years.
The Hindu calendar refers to a set of sidereal solar and lunisolar calendars used in various parts of India. A sidereal solar calendar describes the position of the Earth in its orbit around the Sun with respect to a constellation. The solar calendars like the Tamil and Malayalam calendars emphasise on the sun, while the sun-moon lunisolar calendars like Vikrama and Shalivahana calendars emphasise both the sun and the moon. It is to be noted that the two sets of calendars are offset by a few weeks.
The panchāngam plays a vital role in everyday affairs in many Indian Hindu households to determine the auspicious and inauspicious timings to carry out important tasks, festivals and poojas successfully without any hindrances. In fact, some households consult the panchāngam every single day! This habit is deeply rooted in the belief that events are controlled by effort as well as destiny.
Panchāngam is a Sanskrit word that means "five components/parts". This calendar contains five parameters, namely Vara, Tithi, Nakshatra, Yoga, and Karana, which are determined by studying the Moon's rotation and revolution.
Vāra (वार)
The ancient Indians and Babylonians observed seven heavenly bodies namely, Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn, and named the days after them. Vāra is the measure of the time taken by the Earth to rotate once about its own axis such that the sun appears at the same reference meridian - a solar day. The vāras begin at the first daylight, and seven of these vāras correspond to a cycle, which is what we know as a week.
Tithi (तिथि)
Tithi is the measure of the time interval between consecutive moonrises or high moons. One tithi ends, and another begins when the longitudinal angle difference between the sun and the moon equals an integral multiple of 12°. This also means that there are 30 tithis in one synodic (or lunar) month, the time taken for the moon to revolve around the earth and reach the same angular position with respect to the sun as it had started at the beginning of the month (29 days, 12 hours, 44 minutes, 38 seconds). Since the motion of the moon around the earth, and that of the earth around the sun is a function of its position in the orbit, the 30 tithis start at varying times of the day, and are of varying duration.
Nakṣatra (नक्षत्र)
In the Hindu scriptures, there is a tale that the Moon God (Chandra) was in love with one of the daughters of the Prajāpati Daksha, Rohini. He ended up marrying all 27 of his daughters, the Nakṣatras. Stories aside, nakṣatra is the measure of a 27th part of the ecliptic (the plane of apparent motion of the Sun around the Earth, as observed from the Earth). This corresponds to an angle of 13° 20’ (360°/27). They are named after the asterisms (not constellations!) that lie in the sectors. The time taken by the moon to cross one such sector of the ecliptic is defined as the period of one nakṣatra. This results in an average duration of 24hr for each nakṣatra. The logic behind the number 27 is the length of a sidereal month or the elliptical moon cycle which is approximately 27.3 days.
Yoga (योग)
The word literally means joining or union in Sanskrit. Yoga refers to the time interval during which the combined movement of the sun and the moon or the sum of the individual meridians swept equals the 27th part of the ecliptic, corresponding to an angle of 13° 20’. Thus there are 27 yogas. These are also of varying lengths owing to the non-uniform motion of the moon and sun (apparent).
Karaṇa (करण)
Karaṇa is the measure of half of a tithi, which corresponds to a 6° longitudinal angular difference between the sun and the moon. There are 11 karaṇas in total that can be classified into two groups, four fixed and seven recurring. The four fixed karaṇas each occur only once a month - the night before the new moon, the new moon day and night, and the day after the new moon. The remaining seven recurring karaṇas occur eight times each every synodic month.
Apart from the five parameters involved, the calendars also use terms like pakṣa (पक्ष), māsa (मास), ritu (ऋतु), and saṃvatsara (संवत्सर)
Pakṣa (पक्ष)
A pakṣa (पक्ष) refers to the 14 tithi period on either side of a full moon day, Pūrṇimā (पूर्णिमा) or a new moon day, Amāvásyā (अमावस्या). The waxing fortnight, the period between Amāvásyā and Pūrṇimā is called Śuklapakṣa (शुक्ल पक्ष), and the waning fortnight, the period between Pūrṇimā and Amāvásyā is called Kṛṣṇapakṣa (कृष्ण पक्ष) (in Sanskrit, Śukla means white and Kṛṣṇa means black).
Māsa (मास)
A Hindu month is called a māsa. Irrespective of the type of calendar, a year consists of 12 months. A typical month in the lunar calendar has 30 days that begins on the new moon day, while there are 29 to 32 days in a solar calendar. What the great warrior Bhishma is referring to, is that 12 lunar months make up 354 days, 8 hours, 48 minutes, 34 seconds instead of 365 days, 5 hours, 48 minutes, 46 seconds of the solar year. Thus, the 11 extra days are pushed into the next year, and every 32 months, 16 days and 3 hours, we have an extra month called an adhika māsa (named after the succeeding month) to align the 2 calendars. This is about 2 adhika māsas every 5 years.
Ritu (ऋतु)
This term is used to denote the six seasons observed in India. Every two Hindu months correspond to a season. It begins with Vasanta (वसन्त) or spring and ends with Śiśira (शिशिर) or winter.
Saṃvatsara (संवत्सर)
Varahamihira, a 6th century Indian astronomer, in his encyclopedia Brihat Samhita discussed the concept of saṃvatsara, a “jovian year” (contrary to the solar year that we are familiar with). To add some perspective, a solar year or tropical year is approximately equal to 365 days, 5 hours, 48 minutes, 46 seconds, and is defined by the time taken by the Earth to complete one revolution around the sun. On the other hand, a jovian year is 361 days 0 hours 38 minutes 28 seconds, roughly about 1/12th the time period of Jupiter’s revolution (approximately equal to 11 years, 314 days, 15 hours, 7 minutes, 12 seconds). Thus, there is a difference of about 4.232 days between the solar year and the jovian year, and about every 86 jovian years, a year is skipped to synchronise the 2 calendar years.
The Indian calendar follows a cycle of 60 saṃvatsara from Prabhava (प्रभव) to Akshaya (अक्षय). The rationale behind a 60 year cycle is that, if we assume that the two planets, Jupiter and Saturn, were at the same position at the start of the 1st saṃvatsara, and given that the time period of Jupiter is 11.862 solar yr (~12 jovian yr), and that of Saturn is 29.4571 solar yr (~30 jovian yr), the two planets would reach the same configuration only after 60 jovian years. If we try to visualise the revolution in space, we observe that Jupiter and Saturn sweep 30° and 12° meridians respectively in one Earth year, and hence, would find them at the same meridian every 20 jovian years (and at the original configuration only after 60 jovian years).
Publication and distribution of the Hindu almanac and calendar is a well-established business in India. It is a family business for many families and is passed on from one generation to another. Traditionally these calendars have been published in March/April, corresponding to the Hindu New Year, but some publishers have succumbed to the western tradition of the English New Year to publish the new version.
Unlike the Western Calendar, panchāngam is published in both the calendar and booklet/book formats by several authors, institutions, and societies. Additionally, there are versions of panchāngam that give the data for not just one year, but for a whole century like the Vishvavijaya Panchāngam.
REFERENCES
Understanding of the Panchāngam
Sewell, R., Dikshit, S. B., and Schram, R. (1986) The Indian calendar; with tables for the conversion of Hindu and Muhammadan into A.D. dates, and vice versa; with tables of eclipses visible in India. London: Schwan Sonnenschein & Co., Ltd. Retrieved on August 9, 2020
Rao, S. N., (Feb, 2005) Basics of PANCHANGAM. Achara Vichara Monthly Issue. Shri Vijayadhwaja Jnanapeeta (Regd.) - Shri Pejavara Mutt. Retrieved on August 12, 2020, from
Planetary Science Communications team, JPL (NASA) (n.d.) Planet Compare. NASA’s Science Mission Directorate. Retrieved on August 14, 2020
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