# Islamic calendar

##### Article

November 30, 2021

The Islamic calendar, based on the motion of the Moon, starts from Friday 16 July 622 of the Julian calendar, in which the Hegira by Mohammed (the 1st Muharram of the year 1) was performed, and is divided into 12 lunar months of 29 o 30 days; so that a year lasts 354 days and, approximately every three years, one more day.
Each month begins with the observation of the first crescent of the new moon according to rules that vary according to the different contexts of the Islamic world. For simplicity, however, it will be useful to refer to the 'Islamic tabular calendar', in which the months of 30 and 29 days alternate rigorously (except for the possible addition of a day to the last month of the year).
Often the dating according to this calendar is indicated with the initials h. (from the Arabic hiǧrī 'relating to Hegira') or A.H. (from the Latin Annus Hegirae).

## The months

The (lunar) months are:
Muḥàrram - محرم of 30 days.
Ṣàfar - صفر of 29 days.
Rabīʿ al-àwwal - ربيع الأول of 30 days.
Rabīʿ al-thānī - ربيع الثاني of 29 days.
Jumādā al-àwwal - جمادى الأول of 30 days.
Jumādā al-thāniyya or Jumāda al-akhīra - جمادى الثانية of 29 days.
Ràjab - 30 days رجب.
Shaʿbān - شعبان of 29 days.
Ramaḍān - رمضان of 30 days.
Shawwāl - شوال of 29 days.
Dhū l-qaʿda - ذو القعدة of 30 days.
Dhū l-ḥijja - ذو الحجة of 29 days (30 in "leap" years) The durations of the lunar months are those provided by the Islamic tabular calendar. In practice, they are determined by the observation of the first crescent of the new moon, on the basis of what Mohammed prescribed regarding the duration of the month of Ramadan. The astronomical duration of a lunar month is not constant: it is minimal near the solstice of summer and maximum on the occasion of the winter one. Therefore the month of Ramadan can be 29 days and the month preceding it or the one following it will lengthen to 30.

## "Leap years"

The alternation of months of 29 and 30 days results in an average month duration of 29.5 days (29 days and 12 hours). Since the average duration of the synodic month is 29.530589120 days (approximately 29 days, 12 hours, 44 minutes and 2.9 seconds), with this system the start of the months would be earlier than 8 hours and 48 minutes each year. .
Therefore every three years or so the last month is made to last 30 days instead of the usual 29. The introduction of these "leap" years of 355 days is done on the basis of a cycle of 30 years, in which 11 are leap years: the 2nd , 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th and 29th years. The cycle of thirty years is thus 180 x 30 + 180 x 29 + 11 10631 days, from which derives an average duration of the month of 10631/360 29.53055555 ..... days 29 days 12 hours and 44 minutes exactly. The difference with respect to the synodic month is only 2.9 seconds down, with a resulting error of one day, which would have to be added, approximately every 2483 years.
It is important to note that this correction does not have the function of keeping the Islamic year in some way synchronized with the seasons (which is however impossible for a calendar that is strictly based only on the moon and ignoring the sun), but only to obtain a better synchronization of the beginning of each lunar month with the phases of the moon.
As a consequence of this divergence, the cycle of the twelve lunar months anticipates (it is shorter), each year, by about ten days with respect to the annual solar cycle of the seasons (and therefore with respect to the Gregorian calendar which is optimally synchronized to it); this means that the two cycles have practically no relationship between them (hence, for example, the advance each year of about ten days of the beginning of the month Dhū l-ḥijja).

## Correspondence with the biblical chronology of Eusebius

The date of Hijra corresponds exactly to the first day of the seventh millennium of the Islamic calendar, calculated from the date of creation.