Magnetic load cells that measure force and/or torque are constructed from magnets and one or more arrays of magnetic field sensors. The magnetic field sensors are structured in a tight array where the array is attached to a first portion of a frame. The magnets are operated in pairs polarized in opposition to one-another. In particular, pairs of concentric magnets create sharp field boundaries. The magnets are attached to a second portion of the frame with the magnets separated from the array of field sensors by a small gap. The second portion of the frame is free to displace or rotate in relation to the first portion of the frame when a force or torque is applied to it. The displacement results in a measurable differential change in magnetic field reported by the array that can be sampled and processed to relate to the applied force or torque.