The present invention is a guidance computing system used by the driver of a vehicle towing a trailer while backing-up that rapidly calculates and predicts the direction in which the tow vehicle and trailer will become generally in-line for a given position of the steering wheel, thereby enabling the use of slower, lower cost microcomputers. This is accomplished by using a predetermined table, based on a baseline trailer of known length, having a measure of turning as one of its axes; such an axis is necessary to facilitate ratiometric scaling to convert table values to correspond to any length trailer. In a specially equipped vehicle incorporating servomechanisms to enable the vehicle to steer itself, the driver indicates the direction desired for the trailer to travel. The present invention also predicts left and right path limits for controlling the direction of the trailer when maneuvering complex paths.