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 \to \infty$: 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 \to \infty$, $C$ should decrease to a constant value (which is the case for two spheres separated by a very large distance, where $C = 4\pi\epsilon_0/\left(1/R_1 + 1/R_2\right)$ ), 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 $Q$.