It is not permissible to rely on Calculations in confirming the new Moons

Question :

In some lands of the Muslims the people go about fasting without relying on the sighting of the new moon. Rather, they think it is sufficient to only rely on calendars. So, what is the ruling on this?

Answer:

The Prophet ordered the Muslims that they should:
"Fast according to the sighting of the new moon and break the fast according to its sighting. And if it is hidden from them (due to cloudiness) complete the number as 30 (days)."

This Hadith is agreed upon (i.e., in Al-Bukhari and Muslim). He also said:
"Verily, we are an illiterate nation. We do not write nor do we calculate. The month is like this and this and this," and he withdrew his thumb with the third. Then he said: "The month is like this and this and this," and he held up all of his fingers, meaning that the month is 29 and 30 days.

It is confirmed in Sahih Al-Bukhari from Abu Hurairah that the Prophet said:
"Fast according to its (ie., the new moon's) sighting and break your fast according to its sighting. If it is hidden from you by clouds, complete the number of (days of) Sha'ban as 30."

And he said:
"Do not fast until you see the new moon or you complete the number (of 30 days in Sha'ban), and do not break your fast until you see the new moon or you complete the number (of 30 days in Ramadhan)."

The Hadiths concerning this matter are numerous and all of them prove that it is obligatory to act according to the sighting or completion of the number of days (in the month as 30) when there is no sighting. Likewise they prove that it is not permissible to rely on calculations for this. Shaykhul-Islam Ibn Taimiyyah mentioned that it is the consensus of the people of knowledge that it is not permissible to rely upon calculations to confirm the new moons. This is the truth concerning which there is no doubt. And Allâh is the Giver of success.