The fuel utilization performance of round substrate, planar solid oxide fuel cells with active electrode areas of 19.6, 200, and 500 cm(2) was analyzed. The fuel utilization performance of 0.3 A/cm(2) was consistent with the fuel utilization performance predicted by the Nernst equation, in which air leaking through to the anode was taken into account. The gas permeability coefficient measured through the electrolyte of a cell before and after tests was smaller by an order of four than the calculated value obtained for the gas permeability coefficient at open-circuit voltage, which indicates that air leaked through to the anode around the circumference of the porous anode cell substrate. The observed fuel utilization performance can be explained by the Nernst loss of the water produced by an electrochemical reaction and by air leaking to the anode. Therefore, the gas seal around the circumference of the porous anode cell substrate is especially important for the round substrate, planar solid oxide fuel cell. The permeability coefficient of the gas seal of a solid oxide fuel cell can be estimated from the actual open-circuit voltage by the Nernst equation.