The permittivity of single-crystal single-domain strontium titanate has been measured in detail in the [001], [011], and [111] directions, as a function of temperature (from 4.2 to 300 °K), electric field (from −23 000 to +23 000 V/cm, and frequency (from 1 kHz to 50 MHz). The free energy of the crystal is determined as a function of polarization with temperature as a parameter. The Curie-Weiss law is satisfied in the temperature range 60–300 °K, giving a Curie temperature of 30 ± 2 °K for the three crystal orientations. The Lyddane-Sachs-Teller (LST) relation is satisfied for temperatures between 30 and 300 °K and for electric fields between 0 and 12 000 V/cm. A generalized LST relation is used to calculate the permittivity of strontium titanate from zero to optic frequencies. Two active optic modes are important. The lower-frequency mode is attributed mainly to motion of the strontium ions with respect to the rest of the lattice, while the higher-frequency active mode is attributed to motion of the titanium ions with respect to the oxygen lattice. The restoring forces that act on the Ti ions begin to ``harden'' when these ions are displaced approximately 0.002 Å from their equilibrium positions.