An elevation measuring device comprises a measuring column at which a vertically movable measuring slide is supported, so it can be moved by hand and also by a drive motor through a clutch device. The measuring slide supports a scan head, which imparts a constant measuring force onto the measuring location at the work piece, which is generated by the drive motor and the clutch device. A measuring system detects the elevation coordinate of the scan head and hands said elevation coordinate to a control device for further processing and evaluation. The control device comprises logic for automating the measuring process. This logic automatically detects a positioning of the scan head in a certain direction, which is manually performed by the operator, subsequently controls the drive motor in a suitable manner in order to cause a scanning of the work piece and determines the measurement values.