Forty years ago R.W. Rodieck introduced the Difference-of-Gaussians (DOG) model, and this model has been widely used by the visual neuroscience community to quantitatively account for spatial response properties of cells in the retina and lateral geniculate nucleus following visual stimulation. Circular patches of drifting gratings are now regularly used as visual stimuli when probing the early visual system, but for this stimulus type the mathematical evaluation of the DOG-model response is significantly more complicated than for moving bars, full-field drifting gratings, or circular flashing spots. Here we derive mathematical formulas for the DOG-model response to centered circular patch gratings. The response is found to be given as the difference between two summed series, where each term in the series involves the confluent hypergeometric function. This function is available in commonly used mathematical software, and the results should thus be readily applicable. Example results illustrate how a strong surround suppression in area-summation curves for iso-luminant circular spots may be reversed into a surround enhancement for circular patch gratings. They also show that the spatial-frequency response changes from band-pass to low-pass when going from the full-field grating situation to the situation where the patch covers only the receptive-field center.