One-dimensional tungsten disulfide (WS2) single-walled nanotubes (NTs) with either achiral, i.e., armchair (n, n) and zigzag-type (n, 0), or chiral (2n, n) configuration with diameters d NT > 1.9 nm have been found to be suitable for photocatalytic applications, since their band gaps correspond to the frequency range of visible light between red and violet (1.5 eV < Δεgap < 2.6 eV). We have simulated the electronic structure of nanotubes with diameters up to 12.0 nm. The calculated top of the valence band and the bottom of the conduction band (εVB and εCB, respectively) have been properly aligned relatively to the oxidation (εO2/H2O) and reduction (εH2/H2O) potentials of water. Very narrow nanotubes (0.5 < d NT < 1.9 nm) are unsuitable for water splitting because the condition εVB < εO2/H2O < εH2/H2O < εCB does not hold. For nanotubes with d NT > 1.9 nm, the condition εVB < εO2/H2O < εH2/H2O < εCB is fulfilled. The values of εVB and εCB have been found to depend only on the diameter and not on the chirality index of the nanotube. The reported structural and electronic properties have been obtained from either hybrid density functional theory and Hartree-Fock linear combination of atomic orbitals calculations (using the HSE06 functional) or the linear augmented cylindrical waves density functional theory method. In addition to single-walled NTs, we have investigated a number of achiral double-walled (m, m)@(n, n) and (m, 0)@(n, 0) as well as triple-walled (l, l)@(m, m)@(n, n) and (l, 0)@(m, 0)@(n, 0) nanotubes. All multiwalled nanotubes show a common dependence of their band gap on the diameter of the inner nanotube, independent of chirality index and number of walls. This behavior of WS2 NTs allows the exploitation of the entire range of the visible spectrum by suitably tuning the band gap.