There's a caveat, which is often ignored, to the "easy" equation for parallel plate capacitors C = epsilon * A / d, namely that d must be much smaller than the dimensions of the parallel plate.
Is there an equation that works for large d? I tried finding one and could not. (These two papers talk about fringing fields for disc-shape plates but don't seem to have a valid equation for d -> infinity: http://www.santarosa.edu/~yataiiya/UNDER_GRAD_RESEARCH/Fringe%20Field%20of%20Parallel%20Plate%20Capacitor.pdf and http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.167.3361&rep=rep1&type=pdf)
My hand-waving intuition is that as d -> infinity, C should decrease to a constant value (which is the case for two spheres separated by a very large distance, where C = 4*pi*e0/(1/R1 + 1/R2) ), because at large distances from each plate, the electric field goes as 1/R, so the voltage line integral from one plate to the other will be a fixed constant proportional to charge Q.