The capability calculus is a framework for statically reasoning about program resources such as deallocatable memory regions. Fractional capabilities, originally proposed by Boyland for checking the determinism of parallel reads in multi-thread programs, extend the capability calculus by extending the capabilities to range over the rational numbers. Fractional capabilities have since found numerous applications, including race detection, buffer bound inference, security analyses, and separation logic. However, previous work on fractional capability systems either lacked polymorphism or lacked an efficient inference procedure. Automated inference is important for the application of the calculus to static analysis. This paper addresses the issue by presenting a polymorphic fractional capability calculus that allows polynomial-time inference via a reduction to rational linear programming.