We present a program (spinvert; http://spinvert.chem.ox.ac.uk) for refinement of magnetic diffuse scattering data for frustrated magnets, spin liquids, spin glasses, and other magnetically disordered materials. The approach uses reverse Monte Carlo refinement to fit a large configuration of spins to experimental powder neutron diffraction data. Despite fitting to spherically averaged data, this approach allows the recovery of the three-dimensional magnetic diffuse scattering pattern and the spin-pair correlation function. We illustrate the use of the spinvert program with two case studies. First, we use simulated powder data for the canonical antiferromagnetic Heisenberg model on the kagome lattice to discuss the sensitivity of spinvert refinement to both pairwise and higher-order spin correlations. The effect of limited experimental data on the results is also considered. Second, we re-analyse published experimental data on the frustrated system Y0.5Ca0.5BaCo4O7. The results from spinvert refinement indicate similarities between Y0.5Ca0.5BaCo4O7 and its parent compound YBaCo4O7, which were overlooked in previous analyses using powder data.