We have determined the surface atomic structure of Sc(0001) using quantitative low-energy electron diffraction (LEED). Analysis of LEED intensity-voltage (I-V) spectra using the fully dynamical cavatn code and tensor LEED codes indicates that the first interlayer spacing of Sc(0001) is contracted by (6.1\ifmmode\pm\else\textpm\fi{}1.1)% and that the second interlayer spacing is contracted by (1.1\ifmmode\pm\else\textpm\fi{}1.1)% with respect to the bulk spacing (2.63 \AA{}). This result disagrees with first-principles calculations for the (0001) surface of Sc and only partially agrees with existing knowledge regarding the basal plane of hcp metals. We also present a scanning tunneling microscopy study of a rare-earth surface and discuss the results with respect to the quality of bulk single-crystal rare-earth metal surfaces.