In the 2.5D pocket machining, the pocket geometry (shape of the pocket) significantly affects the efficiency of spiral tool path in terms of tool-path length, cutting time, surface roughness, cutting forces, etc. Hence, the pocket geometry is an important factor that needs to be considered. However, quantitative methods to compare different pocket geometries are scarcely available. In this paper, we have introduced a novel approach for quantitative comparison of different pocket geometries using a dimensionless number, 'DN'. The concept and formula of DN are developed and DN is calculated for various pocket geometries. A concept of percentage utilization of tool (PUT) is also introduced and is considered as a measure and an indicator for a good tool path. The guidelines for comparing pocket geometries based on DN and PUT are reported. The results show that DN can be used to predict quality of tool path prior to tool path generation. Further, an algorithm to decompose pocket geometry into sub-geometries is developed that improves the efficiency of spiral tool path for bottle-neck pockets (or multiple-connected pocket). This algorithm uses another dimensionless number 'HARIN' (HARI is the ?acronym of 'Helps in Appropriate Rive-lines Identification' and suffix 'N' stands for number) to compare parent pocket geometry with sub-geometries. The results indicate that decomposing pocket geometry with the new algorithm improves HARIN and removes the effect of bottle-necks. Furthermore, the algorithm for decomposition is extended for pockets that are bounded by free-form curves.