The geometry of the scroll compressor determines the efficiency of the scroll compressor and controls all elements of its operation. It is therefore critical to be able to accurately model the volumes of the compressor over the course of a revolution. This paper proposes a novel quasi-analytic formulation of the suction, compression and discharge chambers based on a change of variables from involute angle to polar integration angle. This solution has been compared against a reference polygon solution, and for the suction chamber this solution agrees to within 0.02%. The solutions for the compression and discharge chamber volumes are analytic and incur a negligible penalty to overhead of a detailed compressor model. In addition, the general nature of the solution presented allows for multiple compression chambers and more complex discharge geometry.