with one leap day each were needed in 30 years; starting with the day of the Hijra, one can then calculate the conversion between the Islamic calendar and each other calendar. There are two basic uncertainties in the calculated Islamic calendar (Ginzel 1906, Spuler & Mayr 1961): The date of the start of the era, the Hijra, is not certain, probably on AD 622 Jul 15, but possibly on AD 622 Jul 14; it is not clear whether the 15th or 16th year within an intervall of 30 years with 11 leap years would have been picked for inserting one leap day at the end of the last month. Hence, this calendar can deviate by up to two days (Ginzel 1906, Spuler & Mayr 1961, de Blois 2000).\
In addition, it is quite clear that such a calculated Islamic calendar was not in use in historic times, as the famous Arab astronomer [*al-Bīrūnī*]{} (AD 973-1048) wrote: [*the leap years of the Arabs, not that the Arabs ever actually used or use them, but the authors of astronomical tables need them when they construct tables on the basis of the years of the Arabs*]{} (quoted after de Blois 2000). Hence, in 