We analyze total reaction cross sections, $σ_R$, for exploring their sensitivity to the neutron-skin thickness of nuclei. We cover 91 nuclei of O, Ne, Mg, Si, S, Ca, and Ni isotopes. The cross sections are calculated in the Glauber theory using the density distributions obtained with the Skyrme-Hartree-Fock method in 3-dimensional coordinate space. Defining a reaction radius, $a_R=\sqrt{σ_R/π}$, to characterize the nuclear size and target (proton or $^{12}$C) dependence, we find an empirical formula for expressing $a_R$ with the point matter radius and the skin thickness, and assess two practical ways of determining the skin thickness from proton-nucleus $σ_R$ values measured at different energies or from $σ_R$ values measured for different targets.

6 pages, 5 figures, to appear in Phys. Rev. C