Lunar calendar average length of the synodic month is days. Thus it is convenient if months generally alternate between 29 and 30 days (sometimes termed respectively “"hollow"” and “"full"”). The distribution of "hollow" and "full" months can be determined using continued fractions, and examining successive approximations for the length of the month in terms of fractions of a day. In the list below, after the number of days listed in the numerator, an integer number of months as listed in the denominator have been completed: These fractions can be used to construct a lunar calendar, or in combination with a solar calendar
Karkaṭa followed by the solar month of Siṃha. The Karkata month is called "Adi" in the Tamil Hindu calendar. The ancient and medieval era Sanskrit texts of India vary in their calculations about the duration of Karkata, just like they do with other months. For example, the "Surya Siddhanta" calculates the duration of Karkata to be 31 days, 11 hours, 24 minutes and 24 seconds. In contrast, the "Arya Siddhanta" calculates the duration of the Karkata month to be 31 days, 11 hours, 13 minutes and 36 seconds. The Indian solar month names are significant in epigraphical studies of South Asia.