A differential pressure sensor includes a ferrofluid sensing element, or slug, that changes position in a tapered magnetic field in response to a pressure differential. The ferrofluid slug is contained in a tube and moves within the tapered magnetic field, which is perpendicular to the longitudinal axis of the tube. The field has a maximum flux density at its center and tapers off in both axial directions from its center. In response to a pressure differential of zero, the slug is centered in the field. In response to a non-zero pressure differential, the slug moves to the position in the field where the net magnetic forces equal the pressure differential. The position of the slug is sensed by sensing elements which produce output signals that vary according to the position of the slug. In a preferred embodiment the sensing elements are pickup coils that are positioned to encompass the range of movement of one end of the slug, or are a pair of pickup coils positioned, respectively, to encompass the range of movement of the two ends of the slug. The ferrofluid slug thus acts as a movable core for the pickup coil(s). As the ferrofluid slug moves, it changes the relative inductances of the pickup coils. The one coil or the pair of coils are connected in a bridge circuit, which produces an output signal that varies according to the changing inductances, and thus, the pressure differential.