The scaled particle theory of Sato and Teramoto (ST)(1-3) for rigid rods and semiflexible polymers is extended to polymers with a wide range of flexibility. To formulate the free energy of polymer interactions. the polymer molecule is considered to be a collection of freely jointed subchains, envisioned as a series of shorter rods (Kuhn segments). The connectivity between the Kuhn segments is accounted for by using first-order perturbation theory for associating fluids. For polymers with a Kuhn segment number (N) smaller than 1, the model reduces to the ST theory. For polymers with N larger than 1, the model is tested against experimental data for isotropic-nematic phase equilibria. The comparison between the calculated and experimental results is favorable when use is made of experimental persistence length q values and hard-core diameter d values fairly close to those obtained from independent measurements. For flexible chains, the model reduces to a hard-sphere-chain equation of state which has been tested using computer simulation data for compressibility.