A non-linear Grad–Shafranov toroidal equilibrium reconstruction code (MSTFit) has been developed for the Madison Symmetric Torus. This is the first such code applied to the unique magnetohydrodynamic (MHD) equilibrium of the reversed field pinch. A new set of toroidal Green's tables have been computed to impose the boundary condition of the close-fitting conducting shell. The non-linear fitting routine is sufficiently versatile for incorporating data from a variety of internal and external diagnostics, including a novel constraint based on orbits from a heavy ion beam probe diagnostic. Utilizing the full complement of internal and external magnetic and pressure diagnostics, MSTFit resolves accurately subtle changes in internal magnetic structure with implications on MHD stability. We show example equilibria that confirm conservation of magnetic helicity during relaxation and two-dimensional equilibrium effects.