Resonance energy transfer measurements provide a way to estimate distances between chromophores attached to different sites of macromolecules. There are two unknowns involved in resonance energy transfer measurements, the distance between two chromophores and their relative orientation. When static orientational disorder exists, the orientation factor, kappa-2, can vary from 0 to 4, leading to considerable uncertainty in estimation of distances. Fluorescence polarization anisotropy measurements can reduce the degree of uncertainty [Dale & Eisinger (1974) Biopolymers 13, 1573]. There may still be substantial error bounds for the average distance measurements. Time-resolved fluorescence measurements provide an "apparent" average distance and distance distribution containing contributions by both distance and orientation. The contribution of orientation to observed "apparent" average distance and distance distribution widths has been estimated for both simulated and real data. With a single unique distance as input in the simulation and with random but static orientation of donor and acceptor, the recovered average distance is very close to that of the input when the input distance is close to or larger than the Forster distance. The recovered width of apparent distance distribution can be substantial and it changes as a function of Forster distance to average distance ratio and as a function of Forster distance. Similar conclusions apply to the case where there is a real distance distribution. Motional averaging of the orientation was simulated by the Monte Carlo method to estimate the contribution of orientation when chromophores have certain degrees of mobility. As long as there is an apparent distance distribution, be it from angular or real distance distribution or from slow motions, the average distance may be obtained reliably provided the average distance is close to or greater than the Forster distance. The distribution can be measured by time-resolved fluorescence decay studies. When static orientation dominates, the shape of the "apparent" distribution fit depends on Forster distance to average distance ratio. A real distance distribution should have no such dependence.