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Quick facts: The Gregorian Calendar, the most common one in use today, measures the time it takes for the Earth to rotate completely around the Sun, 365.2422 days. It is usually abbreviated CE (or AD) and BCE (or BC). Since 1582 CE, most countries have used the Gregorian Calendar. The Julian Calendar, made official by Julius Caesar in 46 BCE, measures the time it takes for the Earth be under exactly the same constellations, 365.25 days. (It actually takes 365.256 days). In 1582 CE it was 10 days short and abandoned by edict of Pope Gregory XIII, and replaced by the Gregorian calendar above. Lunar Calendars, including Islamic and Jewish calendars, measure the time it takes for the Moon to orbit the Earth 12 times, 354.3667 days. The lunar calendar falls short of the solar calendar by 11 days a year. This deficiency can be made up by occasionally inserting a 13th month, in a method called “intercalation”. The Islamic (Hijri) Calendar is usually abbreviated AH in Western languages from the Latinized Anno Hejirae "In the year of the Hijra." The Jewish Calendar is abbreviated AM from the Latinized Anno Mundi “Year of [the creation of] the World”.

The Islamic calendar is made up of twelve lunar months. The Hijra year is therefore 354.3667 days long. This means that any given month will migrate throughout the solar year. Each Islamic year starts about 11 days earlier each (Gregorian solar) year. The Islamic year is considered to have started at sunset of Thursday, July 15, 622 in the Julian calendar.

The Arithmetic Islamic Calendar has twelve months of alternately 29 and 30 days, the last month having 30 days only in leap years:

	Month	Days
1	Muharram	30
2	Safar	29
3	Rabi' I	30
4	Rabi' II	29
5	Jumada I	30
6	Jumada II	29
7	Rajab	30
8	Sha'ban	29
9	Ramadan	30
10	Shawwal	29
11	Dhu al Qa'da	30
12	Dhu al Hijja	29/30

The leap year occurs in the 2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th and 29th years of a 30 year cycle. A leap year allows the calculated monthly cycle to remain in synch with the appearance of New Moons.

However, the arithmetic Islamic Calendar is not acceptable according to Islamic Law. The beginning of a new month requires physical observation by religious authorities of the new moon. Thus the calculated dates may be off by a day or two and may even vary from country to country. In practice this is most important for the beginning and end of Ramadan, the month of fasting and for the feast of 'Eid al Adha.