A sensing apparatus for characterizing current flow through a conductor includes a plurality of magnetic sensors. In some embodiments, the sensors are grouped in pairs to achieve common mode rejection of signals generated in response to magnetic fields not resulting from current flow through the conductor. Sensors having different levels of sensitivity are used to collect information regarding the magnetic field generated by the current flowing through the conductor, where such information is processed in order to characterize the magnetic field. In some cases the sensors are included on or in flexible material that can be wrapped around the conductor.