Although atomistic simulations of proteins and other biological systems are approaching microsecond timescales, the quality of simulation trajectories has remained difficult to assess. Such assessment is critical not only for establishing the relevance of any individual simulation, but also in the extremely active field of developing computational methods. Here we map the trajectory assessment problem onto a simple statistical calculation of the "effective sample size" -i.e., the number of statistically independent configurations. The mapping is achieved by asking the question, "How much time must elapse between snapshots included in a sample for that sample to exhibit the statistical properties expected for independent and identically distributed configurations?" Our method is more general than standard autocorrelation methods, in that it directly probes the configuration space distribution, without requiring a priori definition of configurational substates, and without any fitting parameters. We show that the method is equally and directly applicable to toy models, peptides, and a 72-residue protein model. Variants of our approach can readily be applied to a wide range of physical and chemical systems.What does convergence mean? The answer is not simply of abstract interest, since many aspects of the biomolecular simulation field depend on it. When parameterizing potential functions, it is essential to know whether inaccuracies are attributable to the potential, rather than undersampling. 1 In the extremely active area of methods development for equilibrium sampling, it is necessary to demonstrate that a novel approach is better than its predecessors, in the sense that it equilibrates the relative populations of different conformers in less CPU time. 2 And in the important area of free energy calculations, under-sampling can result in both systematic error and poor precision. 3To rephrase the basic question, given a simulation trajectory (an ordered set of correlated configurations), what characteristics should be observed if convergence has been achieved? The obvious, if tautological, answer is that all states should have been visited with the correct relative probabilities, as governed by a Boltzmann factor (implicitly, free energy) in most cases of physical interest. Yet given the omnipresence of statistical error, it has long been accepted that such idealizations are of limited value. The more pertinent questions have therefore been taken to be: Does the trajectory give reliable estimates for quantities of interest? What is the statistical uncertainty in these estimates 4-7 ? In other words, convergence is relative, and in principle, it is rarely meaningful to describe a simulation as not converged, in an absolute sense. (An exception is when a priori information indicates the trajectory has failed to visit certain states.)