In this paper, we consider a cloud radio access networks (C-RANs) in which base stations (BSs) are uniformly distributed inside a disk. The outage probability and the ergodic rate achieved by these C-RANs are analyzed, where stochastic geometry is used to capture the randomness of BS locations. Compared with existing studies to C-RANs, more accurate analytical results are developed by applying the Gauss-Chebyshev integration, as confirmed by our simulation results.