  We calculate the diameter and chirality dependences of the binding energies,
sizes, and bright-dark splittings of excitons in semiconducting single-wall
carbon nanotubes (SWNTs). Using results and insights from {\it ab initio}
calculations, we employ a symmetry-based, variational method based on the
effective-mass and envelope-function approximations using tight-binding
wavefunctions. Binding energies and spatial extents show a leading dependence
with diameter as $1/d$ and $d$, respectively, with chirality corrections
providing a spread of roughly 20% with a strong family behavior. Bright-dark
exciton splittings show a $1/d^2$ leading dependence. We provide analytical
expressions for the binding energies, sizes, and splittings that should be
useful to guide future experiments.
