The polarizability circle

•The polarizability of a lossless particle lies on a circle in the complex plane.•When expressed in the polarizability volume, this circle is parameter-free.•We compare several models for the polarizability from the literature.•With dissipation, the polarizability lies asymptotically on a smaller circle. It is shown that the electric dipole polarizability of a small lossless particle lies on a circle in the complex plane, as a consequence of conservation of energy. When expressed in terms of the polarizability volume, this is a parameter-free circle. The center of this polarizability circle is at 3i/4, and its radius is 3/4. The location of the polarizability on the polarizability circle depends on the properties of the particle. For a two-state atom this location is determined by the detuning from resonance. For a material sphere we compare several existing models and check these against the exact solution (Mie scattering), valid for any radius of the particle. We show that when there is dissipation in the particle, the polarizability volume lies asymptotically (large radius) on a reduced polarizability circle. This circle has the same center as the polarizability circle, but it has a smaller radius.