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Islamic-Western Calendar Converter(Based on the Arithmetical or Tabular Calendar)

Introduction

Numerous online Islamic (Hijri) calendar converters can be found on theInternet. They are all based on arithmetical schemes such as those described

below but in most cases the adopted scheme is not specified. The calendar

converter given below incorporates most of the arithmetical conversionschemes described in the literature.

The Arithmetical or Tabular Islamic Calendar

The calendar converter is based on the arithmetical or tabular calendar

introduced by Muslim astronomers in the 9th century CE to (approximately)

predict the begin of the months in the Islamic calendar. The months areassumed to be alternately 30 and 29 days in length resulting in a calendar

year of 354 days.

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. According to the most

commonly adopted method 11 leap days are added in every 30 years. Fourslightly different leap-year schemes have been described in the literature

which are summarized below:

Type Leap years Origin/Usage

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I 2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29Ulugh Beg (15th cent. CE), Kuwaiti

algorithm

II 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29Most commonly used leap-year

scheme

III 2, 5, 8, 10, 13, 16, 19, 21, 24, 27 & 29Some conversion tables of Indian

origin

IV 2, 5, 8, 11, 13, 16, 19, 21, 24, 27 & 30

Habash al-Hsib (9th cent. CE), al-

Brn (10/11th cent. CE), Elias of

Nisibis (11th cent. CE)

Of each calendar scheme two variants are possible depending on whetherthe epoch of the Islamic calendar (1 Muharram, 1 AH) is assumed to be

15 July, 622 CE (known as the Thursday or astronomical epoch) or16 July, 622 CE (Friday or civil epoch).

Western calendar style day month year

CE

Julian day number week day

Arithmetical calendar type day monthyear (A

H)

Ic [15, civil]

Ia [15, astronomical = Kuwaiti algo

rithm]

IIc [16, civil]

IIa [16, astronomical]

IIIc [India, civil]

IIIa [India, astronomical]

IVc [Habash al-Hsib, civil]

IVa [Habash al-Hsib, astronomical

]

Notes on using the Islamic Calendar Converter

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As the Islamic day begins at sunset, the Islamic dates given by this calendar

converter actually begin at sunset of the previous Western date.

Note that the calendar converter can only be used after the year 10 AH

(631/32 CE), the year when the intercalation of extra months in the Arabic

calendar was abolished (Qurn, sra 9:36-37). Before this year, anintercalary month was added to the year every two or three years in order to

keep the calendar in step with the seasons. As the adopted intercalationscheme is unknown, all proposed reconstructions of the calendar before

10 AH are hypothetical.

The Kuwaiti Algorithm

Since a few years Microsoft software includes an Islamic calendar converter

that is based on the so-called Kuwaiti Algorithm. This algorithm isdescribed in several Microsoft web pages 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 thischallenging problem, several years ago some of the top developers in Microsofts MiddleEast Products Division (MEPD) did extensive research into it. They had the longesttimeline of information on the Hijri calendar as is used in Kuwait, and they took thisinformation and did statistical analysis on it, finally arriving at the most accuratealgorithm 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 arithmeticalapproximation (type Ia) which has been used in some Islamic astronomical

tables since the 13th century CE. Naming this algorithm the Kuwaiti

Algorithm is thus historically incorrect and should be discontinued.

Islamic Calendar Converters based on the Calculated First Visibility of

the Lunar Crescent

In many Islamic countries the religious calendar is based on moresophisticated algorithms which predict the first visibility of the lunar

crescent by rigorous calculations of the lunar position with respect to the sun

and the observers horizon.

The Umm al-Qura Calendar of Saudi Arabia: The official calendar

of Saudi Arabia and neighbouring states.

Calendrical Calculations: Based on the algorithms described in

E.M. Reingold & N. Dershowitz, Calendrical Calculations: The

Millennium Edition (Cambridge, 2001) and E.M. Reingold &N. Dershowitz, Calendrical Tabulations 1900-2200 (Cambridge,

2002).

http://quran.al-islam.com/Targama/DispTargam.asp?nType=1&nSeg=0&l=eng&nSora=9&nAya=36&t=enghttp://en.wikipedia.org/wiki/Kuwaiti_algorithmhttp://www.phys.uu.nl/~vgent/islam/mecca/ummalqura.htmhttp://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.htmlhttp://quran.al-islam.com/Targama/DispTargam.asp?nType=1&nSeg=0&l=eng&nSora=9&nAya=36&t=enghttp://en.wikipedia.org/wiki/Kuwaiti_algorithmhttp://www.phys.uu.nl/~vgent/islam/mecca/ummalqura.htmhttp://emr.cs.iit.edu/home/reingold/calendar-book/Calendrica.html

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Islamic Crescents Observation Project (ICOP): Website of the

Arab Union for Astronomy and Space Sciences (AUASS) and the

Jordanian Astronomical Society (JAS) which collects observations of

young lunar crescents and gives predictions of the visibility of the

lunar crescent.

More details on the Islamic calendar and relevant literature are given in my

webpages on theIslamic calendar(at the moment only in Dutch). AnEnglish version will become available in the near future.

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