How the Muslim calendar works

The Muslim year is purely lunar, consisting of twelve months containing, in alternate sequence, thirty and twenty-nine days. Thus it is approximately eleven days shorter than the solar year, with the result that in each cycle of 32.25 years, the individual months pass through all the solar seasons. If, for example, the hajj (which takes place in the last month of the Muslim calendar) occurs at the height of summer, it will occur in the coolest season 16.25 years later, and in the same time again after another 16.25 years.

The twelve months forming the Muslim year are known as Muharram, Safar, Rabi I, Rabi II, Jumada I, Jumada II, Rajab, Shaaban, Ramadan, Shawwal, Dhu al-Qada and Dhu al-Hijja. Thus, 16 July 622 CE was officially declared as 1 Muharram AH 1.

The common year, therefore, has 354 days. But the mean length of a lunar year is 354 days, 8 hours, 48 minutes, 36 seconds, and the period of mean lunation is 29 days, 12 hours, 44 minutes, 3 seconds. This difference of 8 hours, 48 minutes, 36 seconds (which is almost equal to 11/30th of a day), by which the astronomical lunar year is the longer, is compensated by the intercalation of eleven days in every cycle of thirty years at the stated intervals. The most commonly used method of intercalation is to make years 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 in the cycle into leap years, called kabisha. The intercalary day itself is always added to the twelfth month i.e., the month of Dhu al-Hijja which has twenty-nine days in the common year - in a kabisha year it has 30 days. Thus, to determine whether a Muslim year is common or kabisha, divide it by 30. If the remainder is 2, 5, 7, 10, 13, 16, 18, 21, 24, 26, or 29, the year is kabisha, having 355 days; otherwise, it is a common year consisting of 354 days. For instance, AH 1400 gives a remainder 20 and is a common year. AH 1406 (remainder 26) is a kabisha year. A Chronology of Islamic History 570-1000 CE, Ta-Ha Publishers Limited, p 122-23

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