Well, the effective f-stop changes with the pinhole to film plane distance as DWThomas notes.

So that's three numbers, and the physical size of the pinhole, once made, is not a variable (as implied by SMBooth's wording), but a constant.

The 'optimal' pinhole size, however, would change with the distance from film plane to pinhole. Perhaps that's the clarification I'm asking for.

Eric Renner, author of Pinhole Photography and owner of the Pinhole Resource has found over 50 charts from the last 125 years. Although he presents a couple of others, his primary suggestion is:

A=sqrt(55*F)

where A = optimal pinhole diameter in thousandths of an inch
and F = distance from pinhole to film in inches

multiply A by 0.0254 to get pinhole diameter in mm

Lee