A lunar calendar is a calendar based on the monthly cycles of the Moon's phases (synodic months, lunations), in contrast to solar calendars, whose annual cycles are based on the solar year. The most widely observed purely lunar calendar is the Islamic calendar.[a] A purely lunar calendar is distinguished from a lunisolar calendar, whose lunar months are brought into alignment with the solar year through some process of intercalation – such as by insertion of a leap month. The details of when months begin vary from calendar to calendar, with some using new, full, or crescent moons and others employing detailed calculations.
Since each lunation is approximately 29+1⁄2 days,[1] 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),[1] purely lunar calendars are 11 to 12 days shorter than the solar year. In purely lunar calendars, which do not make use of 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).
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For convenience, it is common to speak of a lunar year of twelve synodic months, or 354.36707 days.(which gives a mean synodic month as 29.53059 days or 29 days 12 hours 44 minutes and 3 seconds)