Auto-calibrating current sensor integrated circuits (ICs) are configured for mounting at a position relative to a conductor. The auto-calibrating current sensor ICs can include a plurality of magnetic field sensing elements disposed at different locations within the integrated circuit, respectively, and can be configured to measure a magnetic field produced by a current carried by the conductor. The auto-calibrating sensors can include an electromagnetic model of the IC and the conductor. The model can be operative to determine a magnetic field at points in space due to a given current in the conductor at a known location of the conductor from the IC, and also the inverse situation of determining an unknown current and/or location of the conductor based on measurements of a magnetic field at known locations in space due to an unknown current in the conductor. Related auto-calibration methods are also described.