Achiral compounds 4-methoxy-4-(p-methoxyphenyl)cyclohexanoneethylene ketal (2), 4-hydroxy-4-(p-methoxy phenyl)cyclohexanoneethylene ketal (3), and 3,5-dimethyl-4-nitropyrazole (4) crystallized in chiral structures and the samples showed an enantiomeric excess. We have determined the absolute structures of these compounds by using X-ray diffraction with copper radiation at low temperatures. Moreover, we have also established the prevalent absolute structures in these samples, by comparing their calculated and solid-state vibrational circular dichroism (VCD) spectra. The consistency of this method was confirmed by using (R,R)-2,8-diiodo-4,10-dimethyl-6 H,12H-5,11-methano-dibenzo[b,f][1,5]diazocine, Tröger's base, (R,R)-1, as a chiral compound of known absolute configuration.