SUMMARY For the Poisson regression model, an exact expression for Fisher's information matrix, based upon the moment generating function of the distribution of covariates, is calculated. This parallels a similar, approximate, calculation by Whittemore (1981) for logistic regression. The resulting asymptotic variance of the maximum likelihood estimate of the parameters is used to calculate the sample size required to test hypotheses about the parameters at a specified significance and power. Methods for calculating sample size are derived for various distributions of a single covariate, and for a family of multivariate exponential-type distributions of multiple covariates. The procedures are illustrated with two examples.