Because of the disadvantages in evaluating straightness error of the traditional method, such as high algorithm complexity, low evaluating precision, it can’t be appropriate for various instruments. A fast and accurate method called intercept of convex polygon algorithm is put forward to implement least envelope zone for evaluating plane straightness errors. The algorithm is based on the convex-hull theory in computational geometry, the measuring data of various instruments are firstly converted into coordinate value, then constructed the convex polygon by slope factor. The unique point meeting the least condition can be found, and the straightness error can be calculated through shear shift conversion. Experimental results show that the method is simple and easy for automatic data processing by computer, and has features of high precision and high speed.