Construction measuring device with an automatic plumbing point finding function

The device (10) has a plumb point finding functionality which, after being triggered, runs automatically. The functionality changes the alignment of the sighting unit (13) under automatic control by the evaluation and control unit with the first and/or the second rotary drive and as a function of a known, defined first spatial point (1a) in such a way that precisely one such second spatial point lying on an object surface is approached and marked by the laser beam (14), which lies on a vertical plumb line containing the first spatial point. Independent claims are included for the following: (1) plumb point finding method; and (2) plumb point finding method implementing program recorded computer readable medium.