The isotope Th-229 is unique in that it possesses an isomeric state of only a few electron volts above the ground state, suitable for nuclear laser excitation. An optical clock based on this transition is expected to be a very sensitive probe for variations of fundamental constants, but the nuclear properties of both states have to be determined precisely to derive the actual sensitivity. We carry out isotope shift calculations in Th+ and Th2+ including the specific mass shift, using a combination of configuration interaction and all-order linearized coupled-cluster methods and estimate the uncertainty of this approach. We perform experimental measurements of the hyperfine structure of Th2+ and isotopic shift between Th-229(2+) and Th-232(2+) to extract the difference in root-mean-square radii as delta < r(2)>(232,229) = 0.299(15) fm(2). Using the recently measured values of the isomer shift of lines of Th-229m, we derive the value for the mean-square radius change between Th-229 and its low-lying isomer Th-229m to be delta < r(2)>(229m,229) = 0.0105(13) fm(2).