In fixed-boundary axisymmetric equilibrium calculations the plasma shape is assigned from input. In several circumstances, the plasma shape may not be known a priori, or one may desire to also compute the magnetic field in the volume surrounding the plasma through the calculation of a free-boundary equilibrium. This requires either the coil currents or the magnetic poloidal flux on a curve in the vacuum region to be assigned as input for the free-boundary equilibrium calculation. The FREE-FIX code presented in this article is a general tool for calculating coil currents being given a fixed-boundary calculation. A new formulation is presented, which considerably reduces the computational cost of the calculation. FREE-FIX performs well for different geometries and experiments.