Several methods for estimating the plasma potential and density using cylindrical Langmuir probes are compared to the self‐consistent solutions of the Vlasov–Poisson equations calculated by Laframboise (J. G. Laframboise, Ph. D. dissertation, University of Toronto, 1966). Measurements are made during the decay of a magnetic‐field‐free plasma in which the mean‐free path of the electron is shorter than the dimensions of the vacuum vessel (the electrons, therefore, have a Maxwellian velocity distribution). The measurements are made in a parameter range in which exact analytical solutions do not exist for the ion and electron saturation currents, 0.5≤R/&lgr;De≤5, whereRis the probe radius and &lgr;Deis the electron Debye length (kTe/4&pgr;ne2)1/2. An iterative procedure is used to fit the data at probe voltages both above and below the plasma potential while constraining the curves to be continuous at the plasma potential. The measured curves could be represented extremely well by the numerical results. It is therefore assumed that the plasma parameters used to fit the numerical results to the measurements are correct. The systematic errors which result from using several analysis techniques which assumeR/&lgr;De≪1 are also presented, and it is shown that empirical corrections to these errors can be described which compensate for the finite probe radius.