  Simulations of quantum systems in finite volume have proven to be a useful
tool for calculating physical observables. Such studies to date have focused
primarily on understanding the volume dependence of binding energies, from
which it is possible to extract asymptotic properties of the corresponding
bound state, as well as on extracting scattering information. For bound states,
all properties depend on the size of the finite volume, and for precision
studies it is important to understand such effects. In this work, we therefore
derive the volume dependence of the mean squared radius of a two-body bound
state, using a technique that can be generalized to other static properties in
the future. We test our results with explicit numerical examples and
demonstrate that we can robustly extract infinite-volume radii from
finite-volume simulations in cubic boxes with periodic boundary conditions.
