The application of off-axis aspheres can improve the imaging quality and the compactness of the optical system furthest. The resolving of the best-fit sphere and the material removal, however, is a very important problem during the fabrications. In this paper, an algorithm available for the precise calculation of the conic and high order off-axis asphere is proposed, considering the requirement of minimum material removal and the slope of material removal. The radius of the best-fit sphere, the maximum material removal and the total volume of material removal are calculated by programming. The advantage of the algorithm is shown by the comparison of results derived from new algorithm and empirical equation. At the same time, the application in the off-axis asphere fabrication also proves the correctness of the algorithm. This algorithm is very helpful for the theory and practice of the fabrications of off-axis asphere.