The characterization of the magnetic field distribution is essential in experiments and devices that use magnetic field coil systems. We present an open-source application software, MFV (Magnetic Field Visualizer), for the visualization of the distribution of the magnetic field produced by circular coil systems. MFV models, simulates, and plots the magnetic field of coil systems composed by any number of circular coils of any size placed symmetrically along the same axis. Therefore, any new design or well-known coil system, such as the Helmholtz or the Maxwell coil, can be easily modeled and simulated using MFV. A graph of the homogeneity of the magnetic field can be also produced, showing the work region where the magnetic field is homogeneous according to a percentage of homogeneity given by the user. A standardized input and output file format are employed to facilitate the exchange and archiving of data. We include some results obtained using MFV, showing its applicability to characterize the magnetic field in different coil systems. Furthermore, the magnetic field results provided by MFV were validated by comparing them with results obtained experimentally in a commercial Helmholtz coil. Obtaining the maximum variability between the experimental and simulation magnetic flux density values along the axis of symmetry is 0.87%.