The Tabular Islamic Calendar (also called the Fatimid Calendar) is a rule-based variation of the Islamic calendar. The Islamic calendar or Muslim calendar ( Arabic: التقويم الهجري at-taqwīm al-hijrī; Persian: تقویم هجری قمری It has the same year numbers and months, but the months are determined by arithmetic rules rather than by observation or astronomical calculations. It was developed by early Muslim astronomers of the second hijra century (the eighth century of the common era) to provide a predictable time base for calculating the positions of the moon, sun, and planets. The 8th century is the period from 701 to 800 in accordance with the Julian calendar in the Christian / Common Era. 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. It is used by some Muslims in everyday life.
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 when the 12th and final month has 30 days.
There are 11 leap years in a 30 year cycle. Noting that the average year has 354 11/30 days and a common year has 354 days, at the end of the first year of the 30-year cycle the remainder is 11/30 day. Whenever the remainder exceeds a half day (15/30 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 22/30 day which is reduced to -8/30 day by a leap day. Using this rule the leap years are
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.
The mean month is 29 191/360 days = 29. 5305555. . . days. This is slightly too short and so will be a day out in about 2500 years. The Tabular Islamic calendar also deviates from the observation based calendar in the short term for various reasons.