Prophet Muhammad informed us that such calculation is not relied upon in determining such matters. Imam Ahmad related in his Musnad that the Prophet said:

which means: <<We are a nation which does not depend on writings and calculations [to determine the beginning of the month]. The month is either twenty-nine or thirty days.>> Praise be to Allah, how easy the matter is. Any Muslim with a sound sight can observe the crescent. He does not need to rely on complex calculations only a few people understand.