Abstract: A wellbore inertial directional surveying system for providing a complete directional survey of an oil or gas well borehole to determine the displacement in all three directions of the borehole path relative to the well head at the surface. The information generated by the present invention is especially useful when numerous wells are drilled to different geographical targets from a single off-shore platform. Accurate knowledge of the path of the borehole allows proper well spacing and provides assurance that target formations are reached. The tool is lowered down into a borehole on the electrical cable. A computer positioned on the surface communicates with the tool via the cable. The tool contains a sensor block which is supported on a single gimbal, the rotation axis of which is aligned with the cylinder axis of the tool and, correspondingly, the borehole.