The lunar day
A Tithi is a lunar day, the basic unit of the Hindu calendar. It is defined by the angle between the Moon and the Sun. Each time the Moon pulls 12 degrees ahead of the Sun, as seen along the zodiac, one Tithi is complete. Since a full circle has 360 degrees, a lunar month holds 30 Tithis.
A Tithi is not the same as a calendar day. A calendar day has a fixed length of 24 hours. A Tithi runs from 19 to 26 hours, depending on the speed of the Moon and the Sun at that time of year. It can begin or end at any hour of the day or night. This is why a Panchang lists the start and end times of each Tithi, and why the date of a festival is sometimes unclear at first sight. See What is Panchang?.
Two halves of the month
The 30 Tithis are split into two groups of 15.
Shukla Paksha, the bright half. It runs from the new Moon to the full Moon, when the Moon waxes. The Tithis are numbered 1 to 15, and the fifteenth is Purnima, the full Moon.
Krishna Paksha, the dark half. It runs from the full Moon to the new Moon, when the Moon wanes. The Tithis are again numbered 1 to 14, and the last, number 30 in the full count, is Amavasya, the new Moon.
The same names appear in both halves. A Tithi is therefore named with its half, for example Shukla Panchami or Krishna Panchami.
The names of the Tithis
The 15 names, in order, are Pratipada, Dwitiya, Tritiya, Chaturthi, Panchami, Shashthi, Saptami, Ashtami, Navami, Dashami, Ekadashi, Dwadashi, Trayodashi, Chaturdashi and Purnima or Amavasya.
These names are the Sanskrit numbers from one to fifteen. Pratipada is the first, Dwitiya the second and so on. Ekadashi is the eleventh, and the day of fasting that comes twice a month.
Tithi and the Moon phase
The Tithi is a direct measure of the Moon phase. At the new Moon, the Moon and Sun are in the same place, so the angle is zero. At the end of the seventh Tithi of the bright half the angle is 90 degrees, which is the first quarter. At the full Moon it is 180 degrees. This is why many people say that the Tithi tells you what the Moon looks like in the sky without needing to look.
How the Tithi of the day is chosen
Since a Tithi can start and end at any time, a rule is needed to decide which Tithi names the day. For most purposes, the Tithi that is active at local sunrise gives its name to the day. Some festivals use other rules, such as the Tithi at noon, at sunset or at midnight. Karwa Chauth, for example, depends on moonrise, and Diwali depends on the Amavasya at night.
Sometimes a Tithi does not touch a sunrise at all. It begins after one sunrise and ends before the next. That Tithi is said to be skipped, or kshaya. At other times a Tithi covers two sunrises, and it is said to be repeated, or vriddhi. This is the reason that the number of calendar days in a Tithi month is not always 30.
Tithi and festivals
Most Hindu festivals are fixed to a Tithi in a lunar month, and not to a date. Examples are:
Diwali. The new Moon Tithi, Amavasya, of the month of Kartika or Ashwin, depending on the regional system.
Navratri. The first nine Tithis of the bright half of the month of Ashwin, ending with Dussehra on the tenth.
Ekadashi. The eleventh Tithi in each half of the month, observed with fasting by many.
Maha Shivaratri. The dark fourteenth Tithi of the month of Magha or Phalguna.
Purnima and Amavasya. The full and new Moon days, often marked with prayer, charity or rites for ancestors.
Because the lunar year is about 11 days shorter than the solar year, the dates of these festivals move from year to year on the Gregorian calendar. A leap month is added about once every three years to keep them in season.
Nature of the Tithis
Traditional texts group the Tithis into five types. Nanda Tithis are 1, 6 and 11, said to be joyful. Bhadra Tithis are 2, 7 and 12, said to be good for health and growth. Jaya Tithis are 3, 8 and 13, said to be good for victory and effort. Rikta Tithis are 4, 9 and 14, said to be empty and best avoided for new ventures. Purna Tithis are 5, 10 and 15, said to be complete and favorable. These groupings are part of the muhurta tradition, the choice of timing for events, and they are not a scientific measure.
Using the Tithi in daily life
People who follow the Panchang look at the Tithi for fasts, rituals and the choice of a good day to start work. Others use it simply as a way to track the Moon phase more precisely than the calendar does. If you live outside India, check that your Panchang is set for your own city, because the sunrise that decides the Tithi of the day is local.