Ionic radii and compressibilities have been calculated for a number of monovalent and divalent ions and radicals on the basis of the compressible ion theory. In this theory, the compression energy of an ion is given as a two-parameter function of its radius,A exp (−r/p), the radius and compressibility of the ion being monotonically decreasing functions of the compressing force acting on it. Choosing a standard force reflecting the average environment in the alkali halides, univalent radii and compressibilities have been calculated. This is the first theory to estimate ionic compressibilities. The values show systematic trends among groups of related ions. Anions are found to be significantly more compressible than cations (e.g., the compressibilities of Ca⁺⁺, K⁺, Cl⁻ and S^{− −} are respectively 0.8530, 1.342, 2.952 and 5.150 × 10⁻¹² cm²/ dyne). Multivalent or ‘crystal’ radii and compressibilities have also been calculated by scaling the standard force by the square of the ionic charge. The calculated ionic radii are closer to experimental values than the classical empirical radii.