The complexity of a tool's simultaneous movement in five axes increases the difficulty of evaluating surface error in 5-axis machining. This paper presents an error analysis method for 5-axis machining which applies differential geometry techniques to evaluate the cusp height between adjacent cutter locations. Effective cutting shapes of adjacent cutting positions are derived. The technique of finding cusp height is also proposed. A method of finding the direct and indirect intersection positions is presented to evaluate the surface error. The error analysis method proposed in this paper can be used to improve the efficiency of 5-axis machining and to generate appropriate cutter path distribution. Analytical results and examples of practical applications are also presented.