Electrostatic properties are important for understanding and modeling many phenomena, such as the adsorption of a catalytic metal upon an oxide support. The charge transfer between the metal and the support can lead to positive or negative charges on the metal. Here, the static dipole polarizability is computed for atomic platinum in charge states 0, +1, and −1 in several low-lying electronic terms and levels. Core pseudopotentials are used along with coupled-cluster theory. The best results are estimates for the coupled-cluster CCSDTQ/q-aug-cc-pwCV∞Z-PP values for atomic terms, combined with compositional data from spin–orbit configuration interaction. The polarizability of the anion Pt− is especially challenging for the theory with wildly varying results from different coupled-cluster perturbative approximations such as CCSD(T). For atomic mercury (Hg), selected as a nearby experimental value, our polarizability volume is larger than experiment by 0.8 bohrs3 (or 0.12 × 10−30 m3). For the ground level of neutral platinum, Pt(3D3), we find α0 = (41.2 ± 1.1) bohrs3 or (6.10 ± 0.16) × 10−30 m3. A handful of density functional theory methods are tested and found generally within 10% of our best values.