A simple modification of the filtered backprojection algorithm is presented for the computation of the local statistical noise in emission computed tomography. The technique is general in that any distribution of radioactivity may be accommodated. When applied to positron emission tomography, it is shown that the effects of photon absorption, random coincidences, radioactive decay, and detector nonuniformity may be included. Calculations have shown the effects of resolution, object size, and photon absorption on the statistical noise of disk-shaped emitters. Comparison of calculation and experiment show close agreement both in magnitude and spatial variation. Measurements of the noise level in tomograms of the brain obtained during continuous inhalation of 150-CO2 demonstrate that estimates of radioactivity concentration with a precision of a few percent are readily attainable.