1. A circular shape characteristic measuring device, comprising: a shape measuring device configured to obtain measured data by measuring a profile shape of a circular cross-section of an object to be measured; and a calculator configured to calculate a circular shape characteristic of the circular cross-section based on profile data obtained by applying a rolling circle process and a filtering process to the measured data obtained by the shape measuring device, the calculator comprising: an inputter configured to input an input parameter, the input parameter being one of three parameters including a cutoff value of the filtering process, a minimum number of samples, and a ratio of a radius of the circular cross-section to a radius of a gauge head during the rolling circle process; a parameter table configured to store a relationship between the three parameters, and, based on the input parameter input through the input device, determine the other two parameters of the three parameters; and a sampler configured to perform sampling of the measured data based on the minimum number of samples determined by the parameter table.