We systematically analyze total reaction cross sections of carbon isotopes with N = 6-16 on a 12 C target for wide range of incident energy. The intrinsic structure of the carbon isotope is described by a Slater determinant generated from a phenomenological mean-field potential, which reasonably well reproduces the ground state properties for most of the even N isotopes. We need separate studies not only for odd nuclei but also for 16 C and 22 C. The density of the carbon isotope is constructed by eliminating the effect of the center of mass motion. For the calculations of the cross sections, we take two schemes: one is the Glauber approximation, and the other is the eikonal model using a global optical potential. We find that both of the schemes successfully reproduce low and high incident energy data on the cross sections of 12 C, 13 C and 16 C on 12 C. The calculated reaction cross sections of 15 C are found to be considerably smaller than the empirical values observed at low energy. We find a consistent parameterization of the nucleon-nucleon scattering amplitude, differently from previous ones. Finally, we predict the total reaction cross section of 22 C on 12 C.