In the location estimation problem, translation equivariant estimators are considered. It is shown that under a mild regularity condition the distribution of such estimators is more spread out than a particular distribution which is defined in terms of the sample size and the density of the i.i.d. observations. Some consequences of this so-called spread-inequality are discussed, namely the Cramer-Rao inequality, an asymptotic minimax inequality and the efficiency of the maximum likelihood estimator in some nonregular cases.