With everybody implementing cylindrical coordinate spreadsheet
solutions, I thought I'd better jump in there as well. I had to
learn a few new things and it was highly instructive to examine
John D.'s templates.
My results seem to converge toward about 75 to 80 pF/m for the
capacitance to radius ratio of a thin conducting disk. This is
about 40% higher than the 55.6 pF/m that results from a uniform
(and, therefore, unnaturally constrained) charge distribution.
(I had guessed only 10 to 20% higher.) If my results are correct,
it would seem that an isolated conducting thin disk has about 3/4
the capacitance of a sphere of the same radius.