Summary Response‐history nonlinear dynamic analysis is an analytical tool that often sees use in risk‐oriented earthquake engineering applications. In the context of performance‐based earthquake engineering, dynamic analysis serves to obtain a probabilistic description of seismic structural vulnerability. This typically involves subjecting a nonlinear numerical computer model to a set of ground‐motions that represent a sample of possible realizations of base acceleration at the site of interest. The analysis results are then used to calibrate a stochastic model that describes structural response as a function of shaking intensity. The sample size of the ground‐motion record set is nowadays usually governed by computation‐demand constraints, yet it directly affects the uncertainty in estimation of seismic response. The present study uses analytical and numerical means to investigate the record sample size, n, required to achieve quantifiable levels of mean relative estimation error on seismic risk metrics. Regression‐based cloud analysis in the context of Cornell's reliability method and incremental dynamic analysis using various intensity measures were employed to derive a relation of the form Δ/n, where Δ is a parameter that depends on both the dispersion of structural responses and the shape of the hazard curve at the site. For the cases examined, n can be kept in the 40 to 100 range and achieve 10% mean relative error. The study can contribute to guide engineers towards an informed a‐priori assessment of the number of records needed to achieve a desired value for the coefficient of variation of the estimator of structural seismic risk.