An exact expression is given for the jackknife estimate of the number of species in a community and for the variance of this number when quadrat sampling procedures are used. The jackknife estimate is a function of the number of species that occur in one and only one quadrat. The variance of the number of species can be constructed, as can approximate two-sided confidence intervals. The behavior of the jackknife estimate, as affected by quadrat size, sample size and sampling area, is investigated by simulation.