This paper presents Metrinome, a tool for performing automatic path complexity analysis of C functions. The path complexity of a function is an expression that describes the number of paths through the function up to a given execution depth. Metrinome constructs the control flow graph (CFG) of a C function using LLVM utilities, analyzes that CFG using algebraic graph theory and analytic combinatorics, and produces a closed-form expression for the path complexity as well as the asymptotic path complexity of the function. Our experiments show that path complexity predicts the growth rate of the number of execution paths that Klee, a popular symbolic execution tool, is able to cover within a given exploration depth. Metrinome is open-source, available as a Docker image for immediate use, and all of our experiments and data are available in our repository and included in our Docker image.