The mechanism for prostaglandin G2 synthesis in the cyclooxygenase active site of prostaglandin H synthase has been investigated using hybrid density functional theory (B3LYP). The calculations show that the six-step radical mechanism for the transformation of arachidonic acid to prostaglandin G2 suggested by Hamberg and Samuelsson is energetically feasible. The overall driving force for the reaction starting with the arachidonic acid and the active-site tyrosyl radical is estimated to be about 37 kcal/mol, and two barriers are found to be about 15 kcal/mol, in good agreement with the experimental rate corresponding to a barrier of 14.8 kcal/mol. Competing reactions are also investigated.