Force/torque sensing on hand-held tools enables control of applied forces, which is often essential in both tele-robotics and remote guidance of people. However, existing force sensors are either bulky, complex, or have insufficient load rating. This paper presents a novel force sensing modality based on differential magnetic field readings in a collection of sensor modules placed around a tool or device. The instrumentation is easy to install and low profile, but nonetheless achieves good performance. A detailed mathematical model and optimization-based design procedure are also introduced. The modeling, simulation, and optimization of the force sensor are described and then used in the electrical and mechanical design and integration of the sensor into an ultrasound probe. Through a neural network-based nonlinear calibration, the sensor achieves average root-mean-square test errors of 0.41 N and 0.027 Nm compared to an off-the-shelf ATI Nano25 sensor, which are 0.80% and 1.16% of the full-scale range respectively. The sensor has an average noise power spectral density of less than 0.0001 N/sqrt(Hz), and a 95% confidence interval resolution of 0.063 N and 0.0086 Nm. The practical readout rate is 1.3 kHz over USB serial and it can also operate over Bluetooth or Wi-Fi. This sensor can enable instrumentation of manual tools to improve the performance and transparency of teleoperated or autonomous systems.