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Depending on the method:

"There have been no confirmed sightings of the new crescent in the parameters of the Hilal Committee on the eve of Thursday July 19th, 2012 (29th Shabaan 1433), therefore the Hilal Committee of the GTA officially declares Shaban to complete 30 days and Ramadan will start on Saturday 21st of July, 2012." and

The Fiqh Council of North America recognizes astronomical calculation as an acceptable Shar’i method for determining the beginning of Lunar months including the months of Ramadan and Shawwal. FCNA uses Makkah al-Mukarrama as a conventional point and takes the position that the conjunction must take place before sunset in Makkah and moon must set after sunset in Makkah.

On the basis of this method the dates of Ramadan and Eidul Fitr for the year 1433 AH are established as follows:
1st of Ramadan will be on Friday, July 20, 2012
1st of Shawwal will be on Sunday, August 19, 2012