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A Tithi is a day. A guest is a Tithi. There are 15 Tithi (days) in a fortnight. The uninvited guest does not stay longer than a Tithi; since he is uninvited and does not stay even for a day, he is called A-Tithi and is always welcomed in Indian culture. Half a Tithi is called Karan.

What is a Tithi and How is it Calculated?
One Tithi is one day. In Hindu calendar all days are called Tithi. Hindu calendar is arranged according to Moon and not by Sun.

Thus Tithi is a lunar day which is approximately 1/30th of the time it takes the Moon to orbit the Earth. Thus Tithi is a period in which the difference between the longitudes of Moon and Sun is exactly 12°. All Tithi may begin at varying times of the day and may also vary in duration from approximately 19 to 26 hours.

The Lunar month starts on Pratipadaa Tithi when the Sun and the Moon are at the same longitude. As time progresses, Moon will go ahead of Sun. When Moon's longitude is exactly 12° greater than Sun's longitude, then the first Tithi ends and the second Tithi starts. In general, Tithi may be calculated using the formula:

Take the difference: (Moon's Longitude - Sun's Longitude)
If the value is negative, add 360.
Divide the result by 12, ignore the reminder and take the quotient.
Add 1 to the Quotient which gives the Tithi number as indicated in the table and find out the corresponding Tithi name.

So a Tithi is a lunar day. There are 15 Tithi in the waxing cycle of the Moon (Shukla Paksh), and there are 15 Tithi in the waning cycle of the Moon ( Krishna Paksh). The Tithi is based on a relationship between the Sun and the Moon. The first Tithi (Pratipadaa) is 12 degrees of the Moon away from the Sun, after the new Moon (Amaavasyaa) or full Moon (Poornimaa). The second Tithi is the next 12 degrees of the Moon away from the Sun, 12 to 24 to 36 degrees and so on. A particular day is ruled by the Tithi prevailed on that day at sunrise time, but the Tithi can change anytime of the day or night as it is not based on the solar day but on the situation of the Moon in relation to the Sun. Each Tithi has a name, a ruling planet, and can be used in Muhoort (for picking an auspicious time).

A Lunar month consists of 30 Tithi. The month starts at the start of Padyaami and ends at end of Amaavasyaa. This is when the longitudes of Sun and Moon are exactly the same. This means that the Moon will complete one cycle around the zodiac and catch up with Sun again -

Note:  Why do people not agree on the Tithi of month start?
This statement about the month beginning and its end on Amaavasyaa day seems logical, as the longitude of the Sun and the Moon are the same on that day, but this is more common in southern states of India and Gujaraat. In northern India the month starts from the Pratipadaa after Poornimaa or Poornmaasee (Full Moon) and ends on Poornimaa or Poornmaas. Since the month ends on that day that is why it is called Poornmaas (= full month). By name this also seems logical.

So one Tithi is made of 12 degrees. It shows that each degree is assigned to one of the signs of the Zodiac. In consequences of this, the first degree of the Tithi is Aries, the second degree is Taurus, the third degree is Gemini, and so on. Then the Moon is examined to see in which sign within the Tithi it is placed. Some computer programs give percentages of the Tithi passed at the time of birth. This chart helps one find the sign easily, by seeing the percent of the Tithi passed through at the time of birth.

Calculation of a Tithi
Lunar Tithi are free from Ayanaansh correction and as well as latitude correction, and occur at the same moment throughout the whole world, provided if our computations are on Geo-centric basis.

If Tithi are based on Topo-centric basis , occurrence of moments of Tithi will vary according to latitude as Topo-centric longitude vary up to 1 deg 45 min depending on the latitude and altitude of the place of observation on account of parallax. We must try to lift ourselves from the myth that Soorya Siddhaant value can give better results. Trick lies in method of computation and observation.

That is why if we take Geo-centric sidereal /tropical longitudes, no doubt, ending moment of a Lunar Tithi will occur at the same moment throughout the globe. While the Topo-centric positions slightly differ from place to place depending on the longitude and altitude of the place of observation, maximum being 9 arc sec for Sun, 62 arc min for Moon and 1 arc min for planets. This is the reason, that if Tithi is calculated on the basis of Topo-centric positions, it will vary from place to place. Visibility of the Moon and eclipses are computed with the help of Topo-centric Moon and Sun positions for a place.

The timing of Ingress of Moon or any planet in any Nakshatra or sidereal sign will depend on following factors:
1. Method of computation - Geocentric or Topo-centric
2. First point of sidereal Aries - ie Ayanaansh value.

The name of Lunar months are assigned after the names of prominent stars on the path of the Sun ie  ecliptic. Most of the time Moon's position falls in these stars on the day of occurrence of new-moon day, but this is not a rule.

Types of Tithi
There are several types of Tithi. To know the auspicious Tithi one must know about them.

A-Khand Tithi (undivided)
When one Tithi continues from sunrise to sunset, it is called "A-Khand (undivided) Tithi"
Khandit Tithi (divided)
When any Tithi ends before sunset it is called "Khandit (divided) Tithi"
Kshaya Tithi (destructive)
If there are three Tithi in one day, it is called  (Tithi is destructed) .....  Not good
Adhi-Tithi (excess)
If there is one Tithi distributed in three days, it is called Adhi-Tithi (Excess Tithi)........ Not good
Dashamee Viddhaa Ekaadashee
This is a very special Ekaadashe on which on should not observe fast.

Beneficiary Tithi
There are some Tithi which are good for certain jobs, while others are not good.
Tithi 5 to 10 of both Paksh give average results. Others are considered unfavorable.

Nandaa Tithi
1, 6 and 11 : For Dance, music, house construction, garments, sculpture, wearing or making jewelry, agriculture and festivals.
Bhadraa Tithi
2, 7 and 12 : For Thread ceremony, travel, marriage, ornaments, artistic pursuits, and vehicles.
Jayaa Tithi
3, 8 and 13 : For House building, war-related activities, medication, agriculture, jobs related to weaponry.
Rikt Tithi
4, 9 and 14 : For Use of fire, poison and weapons, cruel deeds, causing injury or death, study of occult, inauspicious pursuits.
Poorn Tithi
5, 10, 15 and 30 : For Marriage, sacred thread ceremony, travel, coronation, and propitiation of planet.

Tithi-Ashtamee
Many people consider Ashtamee Tithi inauspicious for auspicious works.
In an year there are 4 points, which represent change in the travel of Sun. They are December 21/22, March 21/22., June 21/22., and September21/ 22. They are also called as Winter Solstice, Vernal Equinox, Summer Solstice and Autumn Equinox. Similarly in a month there are 4 points, New Moon, Ashtamee, Full Moon and Ashtamee. In the same way, in a day there are 4 points - they are Sunrise, Mid Noon, Sunset and Midnight.

In all these 4 points there is a change in environment and also corresponding change points in living beings. So these 4 points in a day, in a month, and in an year are sacred points and elders advise us to keep us more in the meditation, into seeking Naaraayan, and not to spend time on mundane matters, but to keep one in subtle and spiritual Saadhanaa. That's how usually new ventures of mundane nature are not proposed on these days. Not keeping this point in mind, we only say that these timings are not auspicious for auspicious works - of any kind of mundane proposals. But when it is a work of public use, selfless and productive work, it can be done on any of these days. However if on such a day the Gochar is in favor, a good day is so advocated. The marriages are mostly part of the combined Karm of the couple to go through, if lived without awareness. So they happen, but if we are aware of the ritual and go through the Mantra and their meanings and try to put in to practice, then the marriage is purposeful.

Tithi And Their Devtaa (Lords)
According to Bhavishya Puraan, all Tithi were assigned to different Devtaa to give fruits to their worshippers. Those Devtaa are called Lord of those Tithi and give fruits only when worshipped on those Tithi. These Tithi are assigned like this by Soorya. He has assigned

 

Tithi	Devtaa
Prathamaa	Agni - It is good for all types of auspicious and religious ceremonies
Dwiteeyaa	Brahmaa - It is good for the laying of foundations for buildings and other things of a permanent nature.
Triteeyaa	Kuber - It is good for the cuttings of one's hair and nails and shaving.
Chaturthee	Ganesh - It is good for the destruction of one's enemies, the removal of obstacles, and acts of combat.
Panchamee	Naag - It is favorable for administering medicine, the purging of poisons, and surgery.
Shashthee	Kaarttikeya - It favorable for coronations, meeting new friends, festivities, and enjoyment.
Saptamee	Soorya - It is good to begin a journey, buy conveyances, and deal with other such things as a movable nature.
Ashtamee	Rudra - It is good for taking up arms, building of one's defenses, and fortification.
Navamee	Durgaa - It is suitable for killing enemies, acts of destruction, and violence.
Dashamee	Yam Raaj - It is auspicious for acts of virtue, religious functions, spiritual practices, and other pious activities.
Ekaadashee	Vishwedev Gan - It is good for fasting, devotional activities, and remembrance of the Supreme Lord.
Dwaadashee	Vishnu - It is auspicious for religious ceremonies the lighting of the sacred fire, and the performance of one's duties.
Trayodashee	Kaam Dev - It is good for forming friendships, sensual pleasures, and festivities.
Chaturdashee	Shankar - It is goos for administering poison and calling of elementals and spirits.
Poornimaa	Chandramaa - It is auspicious for merry making, fire sacrifice.
Amaavasyaa	Pitri Gan - It is suitable for the propitiation of the Manes and performance of austerities

Thus if one has to worship Durgaa, he should worship her on Navamee.

Manvantar-aadi (Beginning of the Manvantar) Tithi
There are 14 Manvantar. The 14 Manvantar start on the followings Tithi. All these Tithis are holy for Shraaddh Karm --
(1) Kaartik Shukla 12
(2) Aashwin Shukla 9
(3) Chaitra Shukla 3
(4) Bhaadrapad Shukla 3
(5) Paush Shukla 11
(6) Aashaadh Shukla 10
(7) Maagh Shukla 7
(8) Bhaadrapad Krishn 8
(9) Shraavan Amaavasyaa
(10) Phaalgun Poornimaa
(11) Aashaadh Poornimaa
(12) Kaartik Poornimaa
(13) Jyeshth Poornimaa
(14) Chaitra Poornimaa
[These Amaavasyaa and Poornimaa are according to where the month ends on Amaavasyaa, where the  month ends on Poornimaa, they should take it as its next month.]

Yug-aadi (Beginning of the Yug) Tithi
As there are Manvantar beginning Tithi, there are Yug beginning Tithi also, the followings are the Yug beginning Tithi --
(1) Sat Yug Beginning Tithi - Kaartik Shukla 9
(2) Tretaa Yug Beginning Tithi - Vaishaakh Shukla 3
(3) Dwaapar Yug Beginning Tithi - Maagh Amaavasyaa
(4) Kali Yug Beginning Tithi - Bhaadrapad Krishn 13
[Naarad Puraan, p 327-328]

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