Traditionally, the first day of each month is the day(beginning at sunset) of the first sighting ofthe hilal (crescent moon) shortly after sunset. Besidethat, the astronomical new moon times and dates arealready computed exactly for thousands of yearsbackward and forward. Some nations have used thelunar phase cycle as the basis for their calendars. In amajority of Nadlatul Ulama (NU), oppose the use ofcalculations, on the grounds that the latter would notconform with Muhammad's recommendation toobserve the new moon of Ramadan and Shawwal inorder to determine the beginning of these months. ThisIndonesia‚Äüs largest Muslim organization, prefers toutilize the method called imkanur rukyat, which requiresa clear, visible sighting of the moon. In the other side,Muhammadiyah organization sets the first Ramdhanbased on mathematical and astronomical calculationsknown as hisab wujudul hilal. This article focuses todiscuss further about how Muhammadiyah sets the firstday of Hijrah calendar.