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
Year calculated for 2000, and differences in year lengths, compared to 2000, are given for past and future years. In the tables a day is 86,400 SI seconds long. An average Gregorian year is 365.2425 days (52.1775 weeks, hours, minutes or seconds). For this calendar, a common year is 365 days ( hours, minutes or seconds), and a leap year is 366 days ( hours, minutes or seconds). The 400-year cycle of the Gregorian calendar has days and hence exactly weeks. The Great Year, or equinoctial cycle, corresponds to a complete revolution of the equinoxes around the ecliptic. Its length is