Bandgap fluorescence spectroscopy of aqueous, micelle-like suspensions of SWNTs has given access to the electronic energies of individual semiconducting SWNTs, while substantially lower is the success achieved in the determination of the redox properties of SWNTs as individual entities. Here we report an extensive voltammetric and vis-NIR spectroelectrochemical investigation of true solutions of unfunctionalized SWNTs and determine the standard electrochemical potentials of reduction and oxidation as a function of the tube diameter of a large number of semiconducting SWNTs. We also establish the Fermi energy and the exciton binding energy for individual tubes in solution. The linear correlation found between the potentials and the optical transition energies is quantified in two simple equations that allow one to calculate the redox potentials of SWNTs that are insufficiently abundant or absent in the samples.