The purpose of this article is to provide new guidelines for minimally acceptable preparation taper by developing a theoretical mathematical foundation based on principles of resistance form. Yes and no are the possible answers to the question, "Does a preparation have resistance form?" This dual nature is useful because in graphing resistance form as a function of taper, potential tapers on the x axis are divided into two groups with an exact dividing point. Tapers less than this dividing point provide resistance form; tapers larger or equal do not provide resistance form. This dividing point makes a reasonable standard for minimally acceptable taper. Average tapers are defined as the limiting average taper and are mathematically determined to equal 1/2 arcsin (H/B), where H is the height of the preparation and B is the base. From this equation, the taper required to provide resistance form for an individual preparation can be calculated by using the preparation's height to base ratio. The equation can also be used to provide guidelines by tooth group. Dies of a prosthodontist were saved and sorted by group (incisors, canines, premolars, and molars). Measurements of 30 dies from each of these groups were used to calculate the average (H/B) ratios and standard deviations. Calculating the limiting average taper by using the average height-to-base ratio minus two standard deviations provides the dividing point taper that is acceptable for over 97% of the preparations. The values calculated are: 29 degrees for incisors, 33 degrees for canines, 10 degrees for premolars, and 8.4 degrees for molars.(ABSTRACT TRUNCATED AT 250 WORDS)