A highly precise surface x-ray-diffraction study of the uncovered Cu(001) surface kept at 160 K was carried out. Based on two independent experiments we find that the first (d₁₂) and second (d₂₃) interlayer spacings are contracted by 1.4±0.4 % and expanded by 0.3±0.4 % relative to the bulk value (d_b=1.808 Å), respectively. The root-mean-square (rms) isotropic vibrational amplitude of the top layer atoms (0.095 Å) is enhanced by 80 % over the bulk, rapidly decreasing to 20 % and 5 % for the second and third layers (average values). The rms amplitude top layer vibrations are isotropic within the experimental uncertainty of about 0.02 Å.