It is commonly believed that the full moon falls only on the 14th night of the lunar month and some people use that factor to extrapolate the beginning of the month. It will be useful to understand the technical definition of the full moon and if it appears other than on the 14th night.
What is full moon?
The full moon is the instant of time when the earth is between the moon and the sun in the same vertical plane. This could happen at any moment of the day or night. Therefore, it is very possible that in one month the moon is full at day time and could be 99% lit on the night before. It then becomes full in the morning, but decreases to 99% lit-up on the following night. Such a moon would appear as a full moon to an observer on both the nights. These two nights could be 13th and 14th or 14th and 15th of the lunar month, depending upon the location of the observer on the earth and the birth of the moon (i.e. New Moon Conjunction time).
The time of full moon
As an example, consider the New Moon Conjunction for the lunar month of Dhul Hijjah 1435 AH, which occurred on Wednesday 24th September 2014 at 06:14 hrs UT/GMT. It became a full moon on Wednesday 8th October 2014 at 10:50 hrs UT/GMT, which was daytime in the UK but night time in the USA, as shown in the Day and Night World Map below (timeanddate.com website) below.
The moon may appear full on multiple nights
By calculating the percentage illumination of the moon on the midnight before and the night after the full moon, it was found that the moon would appear full to the naked eye on both the nights of 8th and 9th October 2014, as shown in the Lunar Phase Calendar diagram below (from the moonconnection.com website).
It is also interesting to note that those two nights happened to be 13th and 14th Dhul Hijjah 1435 AH in the UK and USA, who started the month with verified moon sighting news. It is also true to say that in some other lunar months the full moon may fall on the 14th and 15th of the lunar dates.
Therefore, it is incorrect to assume the time of full moon to be on the 14th lunar date only and use that to extrapolate the start date of the lunar month, since the moon may appear to be full to human eye across multiple nights, as explained above.
Note also that all these full moon dates (13th, 14th and 15th) are also known as the days of “white fast” (Ayyam-e-Bid/ایّام البیض), when Prophet Muhammad (sallahu alayhi wasallam) used to keep fast in the middle three days of the lunar months.
When does lunar month start?
The traditional method of starting the lunar month is by looking for the crescent moon after sunset on 29th lunar date by the human eye. If the moon was sighted then the month would start from the next day. Otherwise, 30-days of the month were to be completed, since a lunar month is either 29 or 30 days long (for all normal locations). From a scientific point of view, a lunar month is 29.53 days long and it may become visible to the human eye after sunset either on 29th or 30th day of the month, depending on the location of the observer and the time of New Moon Conjunction. The total number of 29 and 30 days month are approximately 6 months each, respectively (in different combinations), making a total of 354 days lunar year (i.e. 10 days shorter than a solar year).
Possibility of sighting the crescent moon
The crescent visibility map below (from crescentmoonwatch.org) shows the Dhul Hijjah 1435 AH moon was born on Wednesday 24th September 2014 at 6:14 UT/GMT, but it was not possible to be sighted by the human eye on the same evening in Saudi Arabia or anywhere in the whole world. Therefore, the month of Dhul Hijjah 1435 AH was started in the UK and USA from Friday 26th September 2014, making Eid-ul Adha to be on Sunday 5th October 2014.
The civil calendar of Saudi Arabia
The civil calendar of Saudi Arabia (called the “Ummul Qura” calendar) is not based on the visibility of the moon, but on the astronomical formula of, “moonset after sunset at Makkah horizon after New Moon Conjunction”. Therefore, quite often this calendar date biases their witnesses to claim a sighting a day before it is possible to be sighted by the human eye. Unfortunately, this also happened when looking for the Dhul Hijjah 1435 AH moon and Saudi Arabia started the month a day earlier than when the moon was possible to be sighted anywhere in the whole world. Note that some countries simply follow the announcement of Saudi Arabia, especially at the time of Hajj, so their decisions are not a proof of Saudi announcement being correct. [See also the Saudi Dating System]
In conclusion, it is incorrect to extrapolate the start of the lunar month based on the lunar date of the full moon. It is also not correct to justify the erroneous sighting claims of a location/country based on the assumption that the full moon is only on the 14th lunar date.