A tithi is a lunar day. Calculation of tithis is based on the difference of the longitudinal angle between the position of the moon and the sun. There are 30 tithis and a tithi is defined as the time period in which the angular distance of the moon from the sn increases by 12° (1/30 of 360°).
They are numbered beginning with the new moon (in the amanta lunar system). At this point in the moon’s orbit around the earth, the sun and the moon are conjunct, or seen in the sky as together. Thereafter, the moon, in its orbit around the earth, gains in motion over the sun and again apparently meets the sun in the sky at the end of the next new moon. Because the true motions of the moon and the sun are not uniform, tithis are not the same length but vary from day to day. Tithis average about 23.5 hours, but the duration of a particular tithi may be as long as 26.5 hours or as short as 20 hours.
The first fifteen tithis comprise the sukla paksha, literally “bright fortnight,” the period when the moon is waxing. The fifteenth tithi is the full-moon day, Purnima. The dark fortnight, krishna paksha, when the moon is waning, begins after the full moon.
There are fifteen unique tithi names, as the same word is used to describe, for example, the fourth tithi of both the waxing and waning moon. The names of the tithis are: Pratipada (Prathama), Dvitiya, Tritiya, Chaturthi, Panchami, Shasthi, Saptami, Ashtami, Navami, Dasami, Ekadasi, Dvadasi, Trayodasi and Chaturdasi. These repeat, beginning
with Prathama at the beginning of each paksha. The 30th tithi is new-moon day, Amavasya.