On the basis of an improved Thomas-Fermi-Dirac (TFD)-type method, a characteristic radius rD is defined for a free atom or ion, where the electron density acquires the universal value of 0.008714. This value is obtained from the ratio of the Dirac exchange constant to the TF kinetic energy constant. Among vertical groups in the Periodic Table, rD calculated from near-Hartree-Fock densities shows striking linear relationships with the empirical covalent radius, the van der Waals radius, the Wigner-Seitz radius, the ionic radius, the first ionization potential, the electronegativity, the softness, the dipole polarizability and the London dispersion coefficient. The potential at rD due to the net charge inside a sphere of radius rd also varies linearly as Mulliken's electronegativity, among vertical groups. On the average, a sphere of radius rd contains more than 95% of the total electronic charge. The horizontal variations in rd among non-transition, transition, and inner transition atoms are sensitive to the changes in electronic configuration, identifying half-filled and completely filled Subshells and also reflecting the lanthanide contraction. © 1992.