Abstract: The problem of roundness is usually discussed in the system of pole coordinate, but the authors deal with this problem in the system of right-angled coordinate and have developed a new method for calculating roundness. The new method ha.s the advantage of high speed and accuracy, and also the program is simple. It is discussed in the paper whether the extreme value of minimum zone evaluation is unique. Some confusing opinions have been clarified, giving the basis for using direct search methods to calculate the minimum zone value of roundness.