The dates for Umm al-Qura calendar, used by the government of Saudi Arabia for civil purposes, are now determined at the Institute of Astronomical & Geophysical Research of the King Abdulaziz City for Science and Technology (KACST) in Riyadh from modern astronomical theories of the sun and the moon. In the past, the calculation of the Umm al-Qura calendar has been based on the following astronomical rules:
Some sources claim that the computed lunar altitude at sunset had to be at least 9° above the horizon at Mecca but this is not confirmed by the dates listed in a calendar conversion table published in the early 1990s by the King Fahd University of Petroleum & Minerals Research Institute (Dhahran).
In about 17.5% of all cases (between 1356 AH and 1395 AH) the lunar month actually started before the astronomical new moon (Birth of the New Moon) with the lunar crescent already below the horizon at sunset in Mecca (22.0% of all cases). In only 22.2% of all cases could the lunar crescent have been sighted with the naked eye on the first evening of the lunar month.
When the astronomical new moon occurs less than 3 hours after Saudi midnight (equivalent with 0h UT or Greenwich midnight) the lunar month begins at the previous sunset otherwise at the sunset following that.
This is equivalent with a lunar age at the start of the lunar month of approximately 15 hours or less. In about 33.7% of all cases the lunar month actually started before the astronomical new moon with the lunar crescent already below the horizon at sunset in Mecca (43.3% of all cases). In nearly all cases (99.3%) the lunar crescent would have been invisible to the naked eye on the first evening of the lunar month.
On the 29th of the month, the next day is the first day of the [new] month if the moonset is after sunset at Mecca or else the next day is the 30th of the month and [...] the day after is the first day of the new month.
This was equivalent with starting the month on the first evening when moonset occurred after sunset as observed from Mecca, or more precisely, from the Great Mosque of Mecca (al-Masjid al-Harām) where the Kaʾba and the revered Black Stone (al-Hajar al-Aswad) are located.
While these rules insured that the lunar crescent would always be above the horizon at the start of the lunar month it was still possible that this occurred before the astronomical new moon. These anomalous month beginnings can occur when the moon is near its most northerly ecliptic latitude, resulting in moonset occurring after sunset at the latitude of Mecca even before the moment of astronomical new moon. Such cases indeed occurred in Rajab 1421 AH and Shaʿbān 1422 AH, which necessitated the rules to be modified.
If on the 29th day of the lunar month the two following conditions are satisfied, then the next day is the first day of the new lunar month:
- The geocentric conjunction occurs before sunset.
- The moon sets after the sun.
Otherwise, the current lunar month will last 30 days.
Under the current rules the lunar month will always start after the astronomical new moon and with the lunar crescent above the horizon at Mecca (often just barely so). Still, in most cases (about 75%) the lunar crescent will not be visible to the naked eye on the first evening of the lunar month as seen from Mecca (or elsewhere in Saudi Arabia).