The Study of Jyotisha · Chapter 5 of 54 · Part One · Beginnings

#Time and the panchanga

#The Indian almanac

Every Indian household that keeps the festivals keeps a panchanga, an almanac. The word means "five limbs" (pancha, five; anga, limb), because for each day it gives five things:

1. Vara — the weekday;
2. Tithi — the lunar day;
3. Nakshatra — the Moon's star;
4. Yoga — a combined measure of the Sun and Moon;
5. Karana — half a lunar day.

A panchanga also gives sunrise and sunset, the month and year, festivals, and the times of eclipses and of the Sun's entry into each sign. It is the first branch of Jyotisha (astronomy) put to daily use. All of muhurta — the choice of good times — is built from it, and a horoscope always records the panchanga of the birth moment.

This chapter explains each limb, shows how to compute it with nothing more than the longitudes of the Sun and the Moon, and then explains the months, the extra months, and the years. You already know how to find the nakshatra (Chapter 4). The rest is just as easy.

#The day

#Sunrise to sunrise

The Indian day, called the savana ("civil") day, runs from one sunrise to the next. Burgess notes this in his commentary on the Surya Siddhanta (I.12 and I.36), and every panchanga follows it. This is different from the modern civil day, which runs from midnight to midnight. It matters in practice:

• A person born at 3 a.m. on Tuesday by the clock was born, in the Indian reckoning, on Monday, because Tuesday has not yet begun — it begins at Tuesday's sunrise.
• The limbs of the panchanga for "a day" are usually those in force at sunrise. If the tithi changes at 10 a.m., the panchanga names the day after the tithi that was running at sunrise, and gives the time at which it ends.

Because sunrise depends on the place, a panchanga is always for a particular place. Two cities can have different tithis "for the day" when a change falls close to sunrise.

(The Surya Siddhanta itself reckons its astronomical days from midnight at the prime meridian, and says the weekday changes at that moment, adjusted for longitude (Surya Siddhanta I.66). Burgess explains that the commentator reads this only as an instruction for converting times between places. The civil and religious day of the almanacs has always begun at sunrise.)

#Units of time

Indian astronomy divides the day by sixty, just as it divides the circle.

Varahamihira lists these units, from the great age down to the truti, a tiny fraction of a second, among the things every astrologer must know (Brihat Samhita II). You will still see ghatis in traditional horoscopes: "born at 12 ghatis 30 vighatis after sunrise" means 12½ × 24 minutes = 5 hours after sunrise.

Example. Sunrise is at 6:10. A birth is recorded as 7 ghatis 45 vighatis. 7 ghatis = 168 minutes; 45 vighatis = 45 × 24 seconds = 18 minutes. Total 186 minutes = 3 hours 6 minutes. Clock time 6:10 + 3:06 = 9:16.

#Limb 1: Vara, the weekday

The seven weekdays are the same in India as in the West, and are named after the same seven grahas:

The Surya Siddhanta tells how to find the lord of any day by counting days and dividing by seven (Surya Siddhanta I.51–52).

#Why the days come in this order

The order Sun, Moon, Mars, Mercury, Jupiter, Venus, Saturn looks random, but it is not. Burgess explains it in his note to I.51–52:

1. Write the seven grahas in the order of their apparent distance from the Earth in the old astronomy, slowest (farthest) first: Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon.
2. Divide the day into 24 hours. Give the first hour to the day's lord, the second hour to the next graha in the list, and so on, going round the list again and again.
3. The planet that rules the first hour of a day rules the whole day.

Try it. Sunday's first hour goes to the Sun. Hours 1 to 24 of Sunday go Sun, Venus, Mercury, Moon, Saturn, Jupiter, Mars, Sun, Venus, … The 25th hour — the first hour of the next day — falls to the Moon. So Monday follows Sunday. Count on 24 more and you reach Mars: Tuesday. And so on round the week.

These planetary hours are called horas. They are still used in muhurta to choose a good hour for a particular kind of work (Chapter 39). In the Indian reckoning the first hora of the day begins at sunrise, and the horas are often taken as equal divisions of day and night rather than clock hours.

#Limb 2: Tithi, the lunar day

#What a tithi is

The Moon goes round the zodiac faster than the Sun. Starting from new moon, when the two are together, the Moon pulls ahead of the Sun by about 12° a day. When it has gained a full 360°, it is back with the Sun at the next new moon. This cycle — new moon to new moon — is the lunar month, about 29½ days long.

A tithi is the time it takes the Moon to gain 12° on the Sun. Since 360° ÷ 12° = 30, there are 30 tithis in a lunar month. The Surya Siddhanta gives the rule: take the Moon's longitude minus the Sun's longitude, in minutes, and divide by 720 (because 12° = 720′); the result is the number of tithis completed (Surya Siddhanta II.64, II.66).

tithi number = (Moon − Sun) ÷ 12°, then add 1

If Moon − Sun is negative, add 360° first.

#Bright half and dark half

The 30 tithis are divided into two halves of 15 called pakshas ("wings" or "sides"):

• Shukla paksha, the bright half: from new moon to full moon, while the Moon waxes. Tithis 1 to 15. The 15th is Purnima, full moon.
• Krishna paksha, the dark half: from full moon to new moon, while the Moon wanes. Tithis 16 to 30, called 1 to 14 of the dark half, and the 30th is Amavasya, new moon.

The names of the tithis are simply the Sanskrit ordinal numbers, used in both halves:

So "Krishna Ashtami" means the 8th tithi of the dark half — the 23rd tithi of the month. The festival of Krishna's birth, Janmashtami, falls on it in the month of Bhadrapada (or Shravana, depending on the month system — see below).

#The deities and groups of the tithis

Varahamihira gives a presiding deity for each tithi (Brihat Samhita 99.1): Brahma, Vidhata, Hari (Vishnu), Yama, the Moon, Skanda (Subrahmanya), Indra, the Vasus, the Serpents, Dharma, Shiva, Savitri (the Sun), Kama, Kali and the Vishvedevas, for tithis 1 to 15; the new-moon day is sacred to the ancestors (Pitris) (Brihat Samhita 99.2).

He also groups the tithis into five classes (Brihat Samhita 99.2), used constantly in muhurta:

The Rikta ("empty") tithis — the 4th, 9th and 14th — are traditionally avoided for beginning important things. Varahamihira adds that work suited to the deity of a nakshatra may also be done on the tithi of the same deity (Brihat Samhita 99.3).

#Tithis are not all the same length

Because the Moon's speed varies between about 12° and 15° a day, and the Sun's a little, a tithi can last anywhere from about 19 to 26 hours. This has two consequences in the almanac:

• Kshaya tithi ("lost tithi"): a short tithi that begins after one sunrise and ends before the next. No sunrise falls in it, so no day is named after it.
• Vriddhi tithi ("increased tithi"): a long tithi that covers two sunrises, so two days in a row bear its name.

Both are normal and happen several times a year. The calendar on this website marks them.

#Worked example: finding the tithi

The Sun is at 10°00′ Aries (= 10°00′). The Moon is at 2°30′ Leo (= 122°30′).

1. Moon − Sun = 122°30′ − 10°00′ = 112°30′.
2. 112°30′ ÷ 12° = 9.375.
3. 9 tithis are complete, and the 10th is running, 37.5% of the way through.

So the tithi is Shukla Dashami, the 10th tithi of the bright half (since 10 is less than 16). It belongs to the Purna group, and its deity is Dharma.

How long until it ends? The Moon needs to gain another (10 × 12°) − 112°30′ = 7°30′ on the Sun. If the Moon is moving 13°00′ a day and the Sun 0°59′, the Moon gains 12°01′ a day. 7°30′ ÷ 12°01′ ≈ 0.62 days ≈ 15 hours. So Shukla Dashami ends about 15 hours later. This is exactly the method the Surya Siddhanta gives: divide the part still to run by the difference of the daily motions (Surya Siddhanta II.66).

#Limb 3: Nakshatra

You learned this in Chapter 4: divide the Moon's longitude in minutes by 800 (Surya Siddhanta II.64).

In our example, the Moon is at 122°30′ = 7,350′. 7,350 ÷ 800 = 9 remainder 150. The nakshatra is the 10th, Magha, in its first pada.

#Limb 4: Yoga

#What a yoga is

The yoga of the panchanga (not to be confused with the yoga of meditation, or with the planetary combinations also called yogas in horoscopy) is found by adding the longitudes of the Sun and the Moon and dividing the sum into 27 parts of 13°20′ each (Surya Siddhanta II.65).

yoga number = (Sun + Moon) ÷ 13°20′, then add 1

If the sum is more than 360°, subtract 360° first.

The 27 yogas, in the order the Surya Siddhanta's translator lists them, are:

1 Vishkambha · 2 Priti · 3 Ayushman · 4 Saubhagya · 5 Shobhana · 6 Atiganda · 7 Sukarma · 8 Dhriti · 9 Shula · 10 Ganda · 11 Vriddhi · 12 Dhruva · 13 Vyaghata · 14 Harshana · 15 Vajra · 16 Siddhi · 17 Vyatipata · 18 Variyan · 19 Parigha · 20 Shiva · 21 Siddha · 22 Sadhya · 23 Shubha · 24 Shukla · 25 Brahma · 26 Indra · 27 Vaidhriti

Burgess remarks honestly that the yoga is "neither a natural period nor a subdivision of one" and that its use is "chiefly astrological" — but that every almanac carries it (his note to Surya Siddhanta II.65). In muhurta, a few yogas are traditionally avoided for beginnings, especially Vyatipata (17) and Vaidhriti (27), and certain parts of others; Chapter 39 gives the rules.

#Worked example

In our example: Sun 10°00′ + Moon 122°30′ = 132°30′ = 7,950′. 7,950 ÷ 800 = 9 remainder 750. The yoga is the 10th, Ganda, almost finished (750 of 800 minutes done).

#Limb 5: Karana

#What a karana is

A karana is half a tithi — the time it takes the Moon to gain 6° on the Sun (Surya Siddhanta II.69). So there are 60 karanas in a lunar month.

There are only eleven karana names, used in a fixed pattern (Surya Siddhanta II.67–69; Brihat Samhita 99.4–5):

• Four fixed karanas (dhruva or sthira), each used once a month at the same place:
  • Kimstughna: the first half of Shukla Pratipada (tithi 1);
  • Shakuni: the second half of Krishna Chaturdashi (tithi 29);
  • Chatushpada: the first half of Amavasya (tithi 30);
  • Naga: the second half of Amavasya.
• Seven movable karanas (chara), repeating eight times to fill the other 56 half-tithis, beginning with the second half of Shukla Pratipada: Bava, Balava, Kaulava, Taitila, Gara, Vanija, Vishti.

Varahamihira gives the lords of the movable karanas as Indra, Brahma, Mitra, Aryaman, the Earth, Shri and Yama, and of the fixed ones as Kali, the Bull, the Serpent and Vayu (Brihat Samhita 99.4–5). The seventh movable karana, Vishti (also called Bhadra), is traditionally avoided for beginnings.

#Finding the karana

1. Find Moon − Sun as for the tithi.
2. Divide by 6°. The whole number plus one is the karana's place in the month, from 1 to 60.
3. If it is 1, the karana is Kimstughna. If it is 58, 59 or 60, it is Shakuni, Chatushpada or Naga.
4. Otherwise, subtract 2, divide by 7, and look at the remainder: 0 Bava, 1 Balava, 2 Kaulava, 3 Taitila, 4 Gara, 5 Vanija, 6 Vishti.

Worked example. Moon − Sun = 112°30′. 112°30′ ÷ 6° = 18.75 → place 19. 19 − 2 = 17. 17 ÷ 7 = 2 remainder 3 → Taitila.

So the full panchanga for our example moment is:

To complete it you would add the weekday from the calendar date and the time of sunrise at the place.

#Months

#Lunar months and their names

The Indian calendar is lunisolar: its months follow the Moon, but they are kept in step with the Sun's year. A lunar month is named after the nakshatra near which the full moon falls in that month:

#Where a month begins: amanta and purnimanta

There are two traditions for where a lunar month starts:

• Amanta ("ending at the new moon"): the month runs from the day after one new moon to the next new moon. Used in most of South India, Maharashtra and Gujarat.
• Purnimanta ("ending at the full moon"): the month runs from the day after one full moon to the next full moon. Used in most of North India.

The bright halves have the same month names in both systems. The dark halves differ by one: the dark half that is "Bhadrapada Krishna" in the amanta system is "Ashvina Krishna" in the purnimanta system. This is why a festival in the dark half can be described with two different month names in different parts of India, while falling on the same day. The Surya Siddhanta's commentator recognises both reckonings of the month (Burgess's note to Surya Siddhanta I.13).

#Solar months

The calendar also has solar months: a solar month is the time the Sun spends in one sign (Surya Siddhanta I.13). The moment the Sun enters a sign is a sankranti. Makara Sankranti (the Sun's entry into sidereal Capricorn, around 14 January) and Mesha Sankranti (into sidereal Aries, around 14 April) are major festivals. Tamil Nadu, Kerala, Odisha, Assam, Bengal and Punjab keep solar calendars for many civil purposes, with month names that follow the signs.

#The extra month: adhika masa

Twelve lunar months make about 354 days. The solar year is about 365¼ days. Left alone, the lunar months would slip about 11 days a year against the seasons, and festivals would wander round the year. The lunisolar calendar prevents this by adding an extra month about every 32½ months — seven times in nineteen years.

The rule is simple and elegant. Every ordinary lunar month contains one sankranti, because the Sun moves about 30° in a lunar month. But a lunar month (about 29.5 days) is shorter than the average solar month (about 30.4 days). So every few years a lunar month begins just after a sankranti and ends just before the next one. A lunar month in which no sankranti occurs is an extra month, adhika masa, and takes the name of the month that follows it, with adhika ("extra") in front: "Adhika Shravana", for example. The ordinary month that follows is then called nija ("own") Shravana. Festivals are kept in the nija month.

Very rarely the opposite happens: a lunar month contains two sankrantis, and one month name is dropped. This is a kshaya masa ("lost month"). It happens only a few times a century, always in the winter months when the Sun moves fastest.

The Surya Siddhanta counts the intercalary months in its great age as part of its fundamental numbers (Surya Siddhanta I.38–40).

#Years and eras

#The year begins

India has more than one New Year:

• The lunisolar New Year begins on Chaitra Shukla Pratipada, the first day of the bright half of Chaitra (in March or April). It is kept as Ugadi in Karnataka, Andhra Pradesh and Telangana, as Gudi Padwa in Maharashtra, and as the start of the Vikram Samvat year in much of North India.
• The solar New Year begins at Mesha Sankranti (about 14 April), kept as Vishu in Kerala, Puthandu in Tamil Nadu, Pohela Boishakh in Bengal and Baisakhi in Punjab.
• In Gujarat the Vikram Samvat year begins in the autumn, the day after Diwali.

#Eras

Two eras are in common use:

• Vikram Samvat, which runs about 57 years ahead of the common era. The Vikram Samvat year that began in March 2026 is 2083.
• Shaka Samvat, which runs about 78 years behind the common era. The Shaka year that began in March 2026 is 1948. The Indian national calendar uses the Shaka era.

#The sixty-year cycle

Many panchangas also name each year from a cycle of sixty years (samvatsaras), beginning with Prabhava and Vibhava. The cycle is linked to Jupiter, which takes about twelve years to go round the zodiac: five of its orbits make sixty years. (The Surya Siddhanta's rule for "the lord of the year" in I.52 is a separate astrological scheme.) In South India the samvatsara changes at Ugadi; the year that began at Ugadi in March 2026 is Parabhava. North Indian almanacs use a slightly different reckoning tied to Jupiter's actual motion, and so may give a different name.

#Seasons

The year has six seasons (ritus) of two months each: Vasanta (spring), Grishma (summer), Varsha (rains), Sharad (autumn), Hemanta (early winter) and Shishira (late winter). The year is also split into the Sun's northward and southward halves, uttarayana and dakshinayana (Chapter 2).

#Reading a panchanga entry

Here is a typical entry, of the kind you would find in a printed almanac or on the calendar page of this website, with what each part means:

Thursday · Sunrise 6:12 · Sunset 18:21 · Shukla Dashami until 21:40, then Ekadashi · Magha until 14:05, then Purva Phalguni · Yoga Ganda until 8:30, then Vriddhi · Karana Taitila until 9:15, then Gara · Moon in Leo

• The day is Guruvara, ruled by Jupiter, from sunrise at 6:12 to tomorrow's sunrise.
• The 10th tithi of the bright half runs until 9:40 p.m. Tomorrow's sunrise will therefore fall in Ekadashi — a day of fasting for many.
• The Moon is in Magha until 2:05 p.m. and in Purva Phalguni after that; it stays in Leo all day.
• Every limb has its own ending time, and they almost never change together. That is why the almanac gives each one separately.

#Summary

• The Indian day runs from sunrise to sunrise. It has 60 ghatis of 24 minutes; a muhurta is 2 ghatis (48 minutes).
• The weekday lords follow from giving each of the 24 hours to the seven grahas in the order Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon (Surya Siddhanta I.51–52, with Burgess's note).
• Tithi = (Moon − Sun) ÷ 12°; 30 in a lunar month, in a bright half and a dark half (Surya Siddhanta II.66). They are grouped Nanda, Bhadra, Jaya, Rikta and Purna (Brihat Samhita 99.2).
• Nakshatra = Moon ÷ 13°20′ (Surya Siddhanta II.64).
• Yoga = (Sun + Moon) ÷ 13°20′; 27 of them (Surya Siddhanta II.65).
• Karana = half a tithi; four fixed and seven movable names (Surya Siddhanta II.67–69; Brihat Samhita 99.4–5).
• Lunar months are named from the full-moon nakshatra and begin at new moon (amanta) or full moon (purnimanta). A lunar month with no sankranti is an extra month, adhika masa.
• New Year comes at Chaitra Shukla Pratipada (lunisolar) or Mesha Sankranti (solar). The eras are Vikram Samvat and Shaka Samvat, and many almanacs also name the year from a sixty-year cycle.

#Exercises

1. The Sun is at 20°00′ Capricorn and the Moon at 5°00′ Aries. Find the tithi, the yoga and the karana.
2. Sunrise is at 5:45. A birth is recorded at 31 ghatis 15 vighatis. What is the clock time?
3. Using the hour method, which weekday follows Wednesday? Show your counting.
4. A lunar month begins on 17 July and ends on 15 August. The Sun enters sidereal Cancer on 16 July and sidereal Leo on 17 August. Is this an extra month? Why?
5. A festival falls on the 8th tithi of the dark half. In an amanta almanac it is "Shravana Krishna Ashtami". What will a purnimanta almanac call it?

Answers: 1. Sun = 290°, Moon = 5°. Moon − Sun = 5 − 290 = −285 → +360 = 75°. 75 ÷ 12 = 6.25 → tithi 7, Shukla Saptami. Sun + Moon = 295° = 17,700′; ÷ 800 = 22 r 100 → yoga 23, Shubha. 75 ÷ 6 = 12.5 → place 13; 13 − 2 = 11; 11 ÷ 7 = 1 r 4 → Gara. 2. 31 ghatis = 744 minutes; 15 vighatis = 6 minutes; 750 minutes = 12 h 30 m; 5:45 + 12:30 = 18:15. 3. Wednesday's first hour is Mercury; counting 24 hours through Saturn, Jupiter, Mars, Sun, Venus, Mercury, Moon, the 25th hour falls to Jupiter: Thursday. 4. Yes. No sankranti falls between 17 July and 15 August, so the month is adhika. 5. Bhadrapada Krishna Ashtami.