The Arithmetical or Tabular Islamic Calendar

The Islamic calendar converter on this website is based on the ḥisābi calendar, i.e. the arithmetical or tabular calendar, introduced by Muslim astronomers in the 8th century CE to predict the approximate begin of the months in the Islamic lunar calendar. This calendar is sometimes 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 (al-sanat al-basīṭa). In order to keep the calendar in step with the lunar phases every two or three years an extra day is added at the end of the year to the last month resulting in a calendar year of 355 days (al-sanat al-kabīsa).

The 30-Year Intercalation Scheme

According to the most commonly adopted method 11 intercalary days are added in every 30 years (the historical origin for this scheme is explained here).

Several slightly different intercalary schemes have been described in the literature which can be summarized as follows:

Another intercalary scheme – with intercalary years in 2, 5, 8, 10, 13, 16, 18, 21, 24, 26 & 29 – was used in a perpetual calendar inscribed on a now lost astrolabe (IC 127) made in 1212/13 CE (609 AH) by Muḥammad ibn Fattūḥ al-Jamāʾirī of Seville.

Of each intercalary scheme two variants are possible depending on whether the epoch of the Islamic calendar (1 Muḥarram, 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).

The 8-Year Intercalation Scheme

A different scheme, based on an 8-year cycle with intercalary years in 2, 5 & 8, was used in the Ottoman Empire and in South-East Asia. Though less accurate than the 30-year cycle, this cycle was popular due to the fact that within each cycle the calendar dates fall on the same weekdays. In the Dutch East Indies the calendar was reset every 120 years by omitting the intercalary day inserted at the end of the last year.

Islamic Years Which Fall Within a Single Western Year

As the tabular Islamic year slowly cycles through the astronomical seasons, a given year usually partially overlaps two sequential Western years. However, as a tabular Islamic year is about 10 days shorter than a Western year, every 33 or 34 years the tabular Islamic year will completely fall within a single Western year. The following tables indicate which tabular Islamic years (computed with intercalary scheme II and adopting the ‘civil’ or ‘Friday’ epoch) fall within a single Western year.

NB: In earlier versions of this web page it was erroneously claimed that the “Kuwaiti Algorithm”, the forerunner of the present MS HijriCalendar date-conversion software, was based on type I (‘astronomical’). It was actually based on type II (‘astronomical’).

I am grateful to Yoshito Umaoka for pointing out this error.