A series of five experiments used the method of magnitude estimation to assess how height and width are integrated in perceptual and in memorial judgments of area. Separate groups of subjects estimated the areas of perceived or remembered rectangles produced by a symmetrical 4 × 4 factorial design of height and width. Additional independent groups of observers made area judgments, based on special mixes of perceptual and memorial information referring to the height and width components of the to-be-judged rectangles. Both perceptual and memory data obeyed the bilinear interaction prediction of the normative multiplicative model. The relation between perceived and actual area as well as the relation between remembered and actual area could both be described by a compressive power function, with the exponent being reliably smaller for remembered than for perceived area. These results seem to imply a principle of integration rule invariance across perceptual and memorial estimates of a given set of stimuli, in conjunction with characteristically different valuation operations.