The Tabular Islamic calendar () is a rule-based variation of the

Islamic calendar The Hijri calendar (), also known in English as the Islamic calendar, is a lunar calendar consisting of 12 lunar months in a year of 354 or 355 days. It is used to determine the proper days of Islamic holidays and rituals, such as the Ramad ...

. It has the same numbering of years and months, but the months are determined by arithmetical rules rather than by observation or astronomical calculations. It was developed by early Muslim astronomers of the second hijra century (the 8th century of the

Common Era Common Era (CE) and Before the Common Era (BCE) are year notations for the Gregorian calendar (and its predecessor, the Julian calendar), the world's most widely used calendar era. Common Era and Before the Common Era are alternatives to the ...

) to provide a predictable time base for calculating the positions of the moon, sun, and planets. It is now used by historians to convert an Islamic date into a Western calendar when no other information (like the day of the week) is available. Its

calendar era A calendar era is the period of time elapsed since one '' epoch'' of a calendar and, if it exists, before the next one. For example, the current year is numbered in the Gregorian calendar, which numbers its years in the Western Christian era ...

is the

Hijri year The Hijri year () or era () is the era used in the Islamic lunar calendar. It begins its count from the Islamic New Year in which Muhammad and his followers migrated from Mecca to Yathrib (now Medina) in 622 CE. This event, known as the Hij ...

. An example is the

Fatimid The Fatimid Caliphate (; ), also known as the Fatimid Empire, was a caliphate extant from the tenth to the twelfth centuries CE under the rule of the Fatimid dynasty, Fatimids, an Isma'ili Shi'a dynasty. Spanning a large area of North Africa ...

or Misri calendar. It is used by some Muslims in everyday life, particularly in Ismaili and

Shi'a Shia Islam is the second-largest branch of Islam. It holds that Muhammad designated Ali ibn Abi Talib () as both his political successor ( caliph) and as the spiritual leader of the Muslim community ( imam). However, his right is understoo ...

communities, believing that this calendar was developed by Ali. It is believed that when Ali drew up this calendar, the previous events of the earlier prophets also fell into line with this calendar. It is their belief that all Fatimid Imams and their Da'is have followed this tradition. Each year has 12 months. The odd numbered months have 30 days and the even numbered months have 29 days, except in a

leap year A leap year (also known as an intercalary year or bissextile year) is a calendar year that contains an additional day (or, in the case of a lunisolar calendar, a month) compared to a common year. The 366th day (or 13th month) is added to keep t ...

when the 12th and final month Dhu al-Hijjah has 30 days.

Intercalary schemes

30-year cycle

In its most common form there are 11 leap years in a 30-year cycle. Noting that the average year has days and a common year has 354 days, at the end of the first year of the 30-year cycle the remainder is day. Whenever the remainder exceeds a half day ( day), then a leap day is added to that year, reducing the remainder by one day. Thus at the end of the second year the remainder would be day which is reduced to − day by a leap day. Using this rule the leap years are year number 2, 5, 7, 10, 13, 16, 18, 21, 24, 26 and 29 of the 30-year cycle. If leap days are added whenever the remainder ''equals'' or exceeds a half day, then all leap years are the same except 15 replaces 16 as the sixth long year per cycle. The Ismaili Tayyebi community delays three leap days by one year: the third to year 8, the seventh to year 19 and the tenth to year 27 in their 30-year cycle. There is another version where, in addition, the fourth leap day is postponed to year 11 and the last leap day is in the last year of the 30-year cycle. The mean number of days per month in the 30-year cycle is 29.53056 days, or Six months of 29 days and six with 30 days, plus 11 days of the leap years. (29 days × 6 months + 30 days × 6 months) × 30 years + 11 leap days = 10,631 days and 10,631 / 360 = 29.53056 (360 is number of months in 30 years). And this is approximately how long it takes for the moon to make full lunar cycle.

Microsoft Microsoft Corporation is an American multinational corporation and technology company, technology conglomerate headquartered in Redmond, Washington. Founded in 1975, the company became influential in the History of personal computers#The ear ...

's Kuwaiti algorithm is used in

Windows Windows is a Product lining, product line of Proprietary software, proprietary graphical user interface, graphical operating systems developed and marketed by Microsoft. It is grouped into families and subfamilies that cater to particular sec ...

to convert between

Gregorian calendar The Gregorian calendar is the calendar used in most parts of the world. It went into effect in October 1582 following the papal bull issued by Pope Gregory XIII, which introduced it as a modification of, and replacement for, the Julian cale ...

dates and

dates. There is no fixed correspondence defined in advance between the algorithmic Gregorian

solar calendar A solar calendar is a calendar whose dates indicates the season or almost equivalently the apparent position of the Sun relative to the stars. The Gregorian calendar, widely accepted as a standard in the world, is an example of a solar calendar ...

and the Islamic

lunar calendar A lunar calendar is a calendar based on the monthly cycles of the Moon's phases ( synodic months, lunations), in contrast to solar calendars, whose annual cycles are based on the solar year, and lunisolar calendars, whose lunar months are br ...

determined by actual observation. As an attempt to make conversions between the calendars somewhat predictable, Microsoft claims to have created this

algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...

based on statistical analysis of historical data from

Kuwait Kuwait, officially the State of Kuwait, is a country in West Asia and the geopolitical region known as the Middle East. It is situated in the northern edge of the Arabian Peninsula at the head of the Persian Gulf, bordering Iraq to Iraq–Kuwait ...

. According to Rob van Gent, the so-called "Kuwaiti algorithm" is simply an implementation of the standard Tabular Islamic calendar algorithm used in Islamic astronomical tables since the 11th century.

8-year cycle

Tabular Islamic calendars based on an 8-year cycle (with 2, 5 and 8 as leap years) were also used in the Ottoman Empire and in South-East Asia. The cycle contains 96 months in 2835 days, giving a mean month length of 29.53125 days, or 29d 12h 45m. Though less accurate than the tabular calendars based on a 30-year cycle, it was popular due to the fact that in each cycle the weekdays fall on the same calendar date. In other words, the 8-year cycle is exactly 405 weeks long, resulting in a mean of exactly 4.21875 weeks per month.

120-year cycle

In the

Dutch East Indies The Dutch East Indies, also known as the Netherlands East Indies (; ), was a Dutch Empire, Dutch colony with territory mostly comprising the modern state of Indonesia, which Proclamation of Indonesian Independence, declared independence on 17 Au ...

(now Indonesia) into the early 20th century, the 8-year cycle was reset every 120 years by omitting the intercalary day at the end of the last year, thus resulting in a mean month length equal with that used in the 30-year cycles.Gerret Pieter Rouffaer,
Tijdrekening
, in: ''Encyclopaedie van Nederlandsch-Indië'' (The Hague/Leiden: Martinus Nijhoff/E.J. Brill, 1896–1905), vol. IV, pp. 445–460 (in Dutch).

References

Literature

* Marcus Gossler, "Basisformeln zur programmierten Umrechnung einiger astronomischer Kalendertypen", ''Astronomische Nachrichten'', 301 (1980), 191–19
online link
* D.A. Hatcher, "Generalized Equations for Julian Day Numbers and Calendar Dates", ''Quarterly Journal of the Royal Astronomical Society'', 26 (1985), 151–15
online link
* Denis Savoie, "Calcul des concordances entre calendrier musulman et calendrier grégorien ou julien", ''Observations et Travaux (Société astronomique de France)'', 26 (1991), 12–1
online link
*LeRoy E. Doggett, "Calendars", in: P. Kenneth Seidelmann (ed.), ''Explanatory Supplement to the Astronomical Almanac: A Revision to the Explanatory Supplement to the Astronomical Ephemeris and the American Ephemeris and Nautical Almanac'' (Mill Valley A University Science Books, 1992), pp. 575–608 (cf. sections 12.4 & 12.93 for the Islamic calendar
online link
* Jean Meeus, "Jewish and Moslem Calendars", in: ''Astronomical Algorithms: Second Edition'' (Richmond: Willmann-Bell, 1998), chapter 9. * Edward G. Richards, "Calendars", in: S.E. Urban & P. Kenneth Seidelmann (eds.), ''Explanatory Supplement to the Astronomical Almanac: Third Edition'' (Mill Valley A University Science Books, 2013), pp. 585–624 (cf. sections 15.6 & 15.11 for the Islamic calendar). * Edward M. Reingold & Nachum Dershowitz, ''Calendrical Calculations: The Ultimate Edition'' (Cambridge: Cambridge University Press, 2018), chapters 7 & 18.3.

External links

Islamic-Western Calendar Converter (Based on the Arithmetical or Tabular Calendar)
– includes four known variants
Online Alavi Taiyebi Calendar

Calendar Converter
{{DEFAULTSORT:Tabular Islamic Calendar Islamic calendar Dawoodi Bohras Islamic terminology ar:تقويم هجري#التقويم الهجري المجدول