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Tithi
See also       Devtaa of Tithi        Poorv Viddhaa

What is a Tithi and How Is It Calculated?
Day. In Hindoo calendar all days are called Tithi. Hindoo 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. Tithi is a period in which the difference between the longitudes of Moon and Sun is exactly 12°. Tithis may vary in length between 19 and 26 hours.

The Lunar month starts when Sun and 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 then the first Tithi ends and the second Tithi starts. In general, Tithi may 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 Tithis. 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:
This statement about the month beginning and its end on Amaavasyaa day seems logical, but this is more common in southern states and Gujaraat of India. 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).

The Moon is the mother and the Sun is the father. On the material plane, we can see from the Tithi that what was in the mind (Manas) of the mother and father at the time of conception. What is in the mind of the parents at conception is very important in the life of the child. On a spiritual plane we can see what was in the mind (Mahat) of the Divine Mother and Father, or what is the purpose of our creation.

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.

If there are three Tithis in one day, it is called Kshaya Tithi (Tithi is destructed)
If there is one Tithi distributed in three days, it is called Adhi-Tith (Excess Tithi)........ Both are not good

When one Tithi continues from sunrise to sunset, it is called "A-Khand (undivided) Tithi"
When any Tithi ends before sunset it is called "Khand (divided) Tithi"

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 Pratipadaa to Agni, Dwiteeyaa to Brahmaa, Triteeyaa to Kuber, Chaturthee to Ganesh, Panchamee to Naag, Shashthee to Kaartikeys, Saptamee to himself, Ashtamee to Rudra, Navamee to Durgaa, Dashamee to Yam Raaj, Ekaadashee to Vishwedev Gan, Dwaadashee to Vishnu, Trayodashee to Kaam Dev, Chaturdashee to Shankar, Poornimaa to Chandramaa, and Amaavasyaa to Pitar. 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 Tithis. 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 Tithis, there are Yug beginning Tithis also, the followings are the Yug beginning Tithis --
(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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Karan - Half a Tithi is called Karan.

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