Long-term outcome following the Fontan operation may be affected by the amount of energy lost as blood flows through the anastomosis geometry. A method for detailed quantification of energy loss is applied to computational simulations of the flow in an atriopulmonary and a total cavopulmonary model. Five types of flow (near wall, slow recirculation, medium speed vortices, collision, and streamlined flow) are identified and their energy losses quantified. The presence of recirculation regions decreases the efficiency of the atriopulmonary model, and a region of increased energy loss is seen in the collision region in the total cavopulmonary model. However, the most significant energy loss is through wall shear stress, which is maximal in areas where there is rapid, near wall flow.