The determination of the strength of an in-plane magnetic field utilizing one or more magnetically-soft, ferromagnetic member, having a shape, size and material whereas a single magnetic vortex is formed at remanence in each ferromagnetic member. The preferred shape is a thin circle, or dot. Multiple ferromagnetic members can also be stacked on-top of each other and separated by a non-magnetic spacer. The resulting sensor is hysteresis free. The sensor's sensitivity, and magnetic saturation characteristics may be easily tuned by simply altering the material, size, shape, or a combination thereof to match the desired sensitivity and saturation characteristics. The sensor is self-resetting at remanence and therefore does not require any pinning techniques.