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 Förster distance. The recovered width of apparent distance distribution can be substantial and it changes as a function of Förster distance to average distance ratio and as a function of Förster 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.(ABSTRACT TRUNCATED AT 250 WORDS)