Significantly higher accelerations may be predicted for a given return period when acceleration variability is taken into account than when only median acceleration values are used in seismic hazard calculations. If the magnitude range is not restricted, the acceleration having a given return period increases from a (sub o) , obtained using median values, to a (sub o) exp(beta sigma (super 2) /2c (sub 2) ), when acceleration variability is included. This result assumes the attenuation function is of the form log (sub e) (a) = c (sub 1) +c (sub 2) m+f(R) [where f(R) is a function of distance only], and the magnitude-frequency relationship is log (sub e) (N) = alpha -beta m. In this case, the acceleration for a return period is best approximated by using the acceleration that is a factor exp(ksigma ) greater than the median, where k = beta sigma /2c (sub 2) . For a restricted magnitude range, m (sub min) 〈 or =m〈 or =m (sub max) , using only median values limits the calculated accelerations at a site to a range a (sub min) 〈 or =a〈 or =a (sub max) . If variability is included, the acceleration range is no longer limited; the return period of an acceleration near a (sub min) increases, while that of an acceleration near a (sub max) decreases. If the distribution of accelerations is truncated at nsigma , the maximum acceleration at a site will be a (sub max) exp(nsigma ). Half or more of the increase in the acceleration level for a return period obtained by including acceleration variability may result from accelerations that are greater than 1.5sigma to 2.0sigma above the median value. Including variability and using a finite maximum magnitude may give a higher acceleration for a fixed return period than the value calculated using median values and an infinite maximum magnitude.--Modified journal abstract.