Fundamental antenna limits of the gain-bandwidth product are derived from polarizability calculations. This electrostatic technique has significant value in many antenna evaluations. Polarizability is not available in closed form for most antenna shapes and no commercial electromagnetic packages have this facility. Numerical computation of the polarizability for arbitrary conducting bodies was undertaken using an unstructured triangular mesh over the surface of 2D and 3D objects. Numerical results compare favourably with analytical solutions and can be implemented efficiently for large structures of arbitrary shape.