Investigation the Arithmetical or Tabular Islamic calendar

Peer review under responsibility of National Research Institute of Astronomy and Geophysics.

Figures & data

Table 1 Leap years in each 30-year cycle and its usage.

Type	Leap years with 355 days in each 30-year cycle	Origin/usage
I	2, 5, 7, 10, 13, 15, 18, 21, 24, 26 & 29	Kuwaiti algorithm
II	2, 5, 7, 10, 13, 16, 18, 21, 24, 26 & 29	al-Fazārī, al-Khwārizmī, al-Battānī.(the most popular form)
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, al-Bīrūnī, Elias of Nisibis

Fig. 1 The suggested Arithmetical calendar after immigration.