Lunar calendar

A lunar calendar is a calendar whose months record the cycles of the Moon's phases (synodic months, lunations). This in contrast to solar calendars, whose annual cycles are based on the solar year (which is about 11 to 12 days longer than twelve lunar months). It is also to be contrasted with lunisolar calendars, which also count lunar months but recover the accumulated differences by adding ("intercalating") a thirteenth leap month every few years. The most widely observed lunar calendar is the Islamic calendar.

Since each lunation is approximately 29+1⁄2 days, it is common for the months of a lunar calendar to alternate between 29 and 30 days. Since the period of 12 such lunations, a lunar year, is 354 days, 8 hours, 48 minutes, 34 seconds (354.36707 days), lunar calendars are 11 to 12 days shorter than the solar year. In lunar calendars, which do not make use of lunisolar calendars' intercalation, the lunar months cycle through all the seasons of a solar year over the course of a 33–34 lunar-year cycle (see, e.g., list of Islamic years). The details of when months begin vary from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations. The term lunar new year is the first day of lunar calendar but is also widely used, especially in the US, of lunisolar new years.