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The Islamic (hijri) calendar is used by more than a billion Muslims around the world to determine the main days of observance in the Islamic religious year. Although in daily life the Western (Gregorian) calendar is now usually followed, the Islamic lunar calendar has since the days of the prophet Muhammad regulated the key days in the Islamic year such as the start and end (‛Īd al-Fitr) of the month of fasting (Ramadān) and the Day of Sacrifice (‛Īd al-Adhā on 10 Dhū ’l-Hijja) during the annual pilgrimage (hajj) at Mecca.
Numerous online Islamic calendar converters can now be found on the internet, but in many cases it is unclear on which algorithm they are based. Most of these online calendar converters are based on arithmetical schemes such as those described below but often the adopted calculation scheme is not specified in detail.
The Islamic calendar converter given below incorporates most of the arithmetical conversion schemes described in the literature or found on the internet. The Islamic calendar converter will be useful for determining the approximate Western equivalent for an Islamic calendar date (for conversion programs and tables based on the first sighting of the lunar crescent, see the links given at the bottom of this webpage) and can also be used for converting historical Islamic calendar dates to Western calendar dates.
The following Islamic calendar converter is based on the hisabi calendar, i.e. the arithmetical or tabular calendar, introduced by Muslim astronomers in the 9th century CE to predict the approximate begin of the months in the Islamic lunar calendar. This calendar is also often referred to as the Fātimid calendar but this is in fact one of several almost identical tabular Islamic calendars.
The months in the tabular Islamic calendar are assumed to be alternately 30 and 29 days in length resulting in a normal calendar year of 354 days (sanā basīta). In order to keep the calendar in step with the lunar phases every two or three years an extra day is added to the last month resulting in a calendar year of 355 days (sanā kabīsa). According to the most commonly adopted method 11 intercalary days are added in every 30 years (the historical origin for this scheme is explained below).
Four slightly different intercalary schemes have been described in the literature which can be summarized as follows:
| Type | Intercalary years with 355 days | Origin/Usage |
| I | 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29 | Kūshyār ibn Labbān (11th cent. CE), Ulugh Beg (15th cent. CE), “Kuwaiti Algorithm” |
| II | 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29 | Most commonly used leap-year scheme |
| III | 2, 5, 8, 10, 13, 16, 19, 21, 24, 27 & 29 | Fātimid calendar (also known as the Misri or Bohra calendar) |
| IV | 2, 5, 8, 11, 13, 16, 19, 21, 24, 27 & 30 | Habash al-Hāsib (9th cent. CE), al-Bīrūnī (10/11th cent. CE), Elias of Nisibis (11th cent. CE) |
Of each intercalary scheme two variants are possible depending on whether the epoch of the Islamic calendar (1 Muharram, 1 AH) is assumed to be 15 July, 622 CE (known as the ‘astronomical’ or ‘Thursday’ epoch) or 16 July, 622 CE (the ‘civil’ or ‘Friday’ epoch).
As the Islamic day begins at sunset, the Islamic dates given by this calendar converter actually begin at sunset of the previous Western calendar date.
Note that the Islamic calendar converter should not be used before the year 10 AH (631/32 CE), the year when the intercalation of extra months in the Arabian calendar was abolished (Qur’ān, sūra 9:36-37). Before this year, an intercalary month was added to the year every two or three years in order to keep the calendar aligned with the seasons. As the adopted intercalation scheme is uncertain, all proposed reconstructions of the Islamic calendar before 10 AH can only be regarded as hypothetical.
For this reason, Western calendar dates commonly cited for key events in early Islam such as the hijra, the Battle of Badr, the Battle of Uhud and the Battle of the Trench, should be viewed with caution as they can be in error by one, two or even three lunar months.
Many sources erroneously claim that the hijra, the date on which Muhammad and a small number of his companions secretly left Mecca, and after a journey of some two weeks arrived in Yathrib (later to be known as Madinat al-Nabī [‛The City of the Prophet’], Medina in English), occurred on 1 Muharram, 1 AH. However, the date of the hijra is not mentioned in the Qur’ān or in other early Islamic texts. Later traditions, such as mentioned in the hadith (collections of sayings and actions of the prophet and his companions), early biographies of Muhammad and Islamic astronomical/chronological tables suggest that the hijra occurred in the last week of the month Safar (probably on the 24th) and that Muhammad and his companions arrived at the outskirts of Yathrib on the 8th day of the month Rabī‘ al-Awwal on a day when the Jews of Yathrib were observing a day of fasting, and after resting for a few days, entered Yathrib on the 12th day of month Rabī‘ al-Awwal.
Converted to the Julian calendar, and taking into account the intercalary months (probably three) which were inserted between the hijra and the last pilgrimage of Muhammad (10 AH), the hijra probably occurred on Thursday, 10 June (622 CE), and Muhammad’s arrival at the outskirts of Yathrib probably occurred on Thursday, 24 June (622 CE). Muhammad’s entry into Yathrib probably occurred on Monday, 28 June (622 CE).
Early Islamic astronomy was largely based on that of the Hellenistic astronomer Claudius Ptolemy of Alexandria (fl. 150 CE) and the astronomical tables in his Almagest served as the basis of many similar Islamic astronomical tables. For the length of a lunation – the average interval from new moon to new moon – Ptolemy adopted the value of 29;31,50,8,20 days (expressed in sexagesimal notation) which had been used during the last few centuries before the Common Era by Babylonian astronomer-priests. The same value is still used in the present-day Hebrew calendar (where it is expressed as 29d 12h 793p) and is equivalent with 29d 12h 44m 3⅓s in modern time units.
From this value, the length of a lunar year with 12 lunations results in 354;22,1,40 days which can be approximated without great loss of accuracy to 354;22 days. Thus by adding 22 intercalary days in every 60 years – or equivalently, 11 intercalary days in every 30 years – a tabular lunar calendar can be constructed which on average will closely follow the visible phases of the moon for several millennia.
A complete 30-year cycle contains (19 × 354) + (11 × 355) = (30 × 354) + 11 = 10631 days or 1518 weeks and five days. Thus after seven 30-year cycles (or 210 years) the weekdays will repeat exactly again on the same days in the tabular lunar calendar. For this reason medieval Islamic calendrical tables are often given for a period of 210 years.
The following online or downloadable calendar converters can be grouped as:
Scheme Ic
Scheme Ia
Scheme IIc
Scheme IIIa
Since a few years Microsoft software includes an Islamic calendar converter based on the so-called “Kuwaiti Algorithm”. This algorithm is described in Microsoft webpages as:
The Hijri calendar is very important to Saudi Arabia and other countries such as Kuwait, and thus this seemingly unsolvable problem must be solved. In an effort to solve this challenging problem, several years ago some of the top developers in Microsoft’s Middle East Products Division (MEPD) did extensive research into it. They had the longest timeline of information on the Hijri calendar as is used in Kuwait, and they took this information and did statistical analysis on it, finally arriving at the most accurate algorithm they could devise.
Microsoft gives no details on the mathematics of the “Kuwaiti Algorithm” but one can easily demonstrate that it is based on the standard arithmetical scheme (type Ia) which has been used in Islamic astronomical tables since the 11th century CE. Naming this algorithm the “Kuwaiti Algorithm” is thus historically incorrect and should be discontinued.
In many Islamic countries the religious calendar is actually based on more sophisticated algorithms which predict the first visibility of the lunar crescent by rigorous calculation of the moon’s position with respect to the sun and the observer’s horizon. The thus predicted dates can differ up to one or two days with those of the tabular Islamic calendar described above.
More details on the Islamic calendar and relevant literature are given in my webpages on the Islamic calendar (at the moment only in Dutch). An English version will become available in the near future.
