Sahih Muslim Book 6, Hadith Number 2366.

Chapter : Fasting in Ramadan should necessarily be commenced with the sight of the new moon and finished with the sight of the new moon. If the weather is cloudy at the beginning or at the end, then complete thirty days.

‘Ubaidullah narrated on the authority of the same chain of transmitters that the Messenger of Allah (may peace be upon him) made a mention of Ramadan and said: The month may consist of twenty-nine days, and it may be thus, thus and thus, and (he further) said: Calculate it, but he did not say thirty.