The spatial orientation of a geological feature is commonly specified by the dip angle and azimuth of the fall line. Both angles are measured using a geological compass (GC). A conventional GC needs to be levelled before the magnetic azimuth can be read. We have developed a digital geological compass (DiGC) that does not require levelling; it can be manufactured small and lightweight, and yields accurate dip angle and azimuth measures within less than a second. We introduce the concept of such a DiGC, based on an assembly of three accelerometers and three magnetometers, discuss the computation of dip angle and azimuth, and present results from a series of test measurements confirming that a precision of better than 1° (1σ) can be obtained.