A robotic system includes a dexterous robot having robotic joints, angle sensors adapted for measuring joint angles at a corresponding one of the joints, load cells for measuring a set of strain values imparted to a corresponding one of the load cells during a predetermined pose of the robot, and a host machine. The host machine is electrically connected to the load cells and angle sensors, and receives the joint angle values and strain values during the predetermined pose. The robot presses together mating pairs of load cells to form the poses. The host machine executes an algorithm to process the joint angles and strain values, and from the set of all calibration matrices that minimize error in force balance equations, selects the set of calibration matrices that is closest in a value to a pre-specified value. A method for calibrating the load cells via the algorithm is also provided.