How the beginning of Ramadan calculated?

The responsibility of fasting the month of Ramadan becomes incumbent upon the occurrence of one of two matters:
to sight the crescent of Ramadan after the sunset of the 29th day of Sha^ban (the month directly preceding Ramadan) or, if the crescent is not seen, then completing 30 days of Sha^ban.
So, the beginning of the month of Ramadan, as well as the end of the month is determined by sighting the crescent, and if not cited, then by completing the month with 30 days--as is the case with determining all the months of the lunar calendar. This is taken from the hadith of the Prophet related by al-Bukhariyy and Muslim : The Hadith means,
(Do not fast one or two days before Ramadan. Start the month when you see the crescent and end the month when you see the crescent. If you are blocked from seeing it, complete Sha^ban thirty days.)
So, on the 29th day of Sha^ban, directly after the sun sets, the Muslims look towards the western horizon, and if the crescent (of the new moon) is seen, the following day will be the first day of Ramadan. If it is not seen, because of cloud cover or another reason, then the next day will complete 30 days of Sha^ban, and the day after that is the first day of Ramadan.
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