It is known that electric and magnetic parts of the Weyl tensor in General Relativity are analogous to that occur in the theory of electromagnetism. On the other hand, Newman-Penrose formalism provides a new dimension to the solutions and interpretations for the theory of relativity. Its significance in understanding spacetimes with some particular Petrov types, solutions with different material contents is well known. This paper provides spin coefficient form of electric and magnetic parts of the Weyl tensor, which leads to a new and efficient way for the computation of electric and magnetic parts of the Weyl tensor. It is observed that the computational time is greatly reduced when done using computer algebra system in comparison to that is done manually. This technique is elaborated in the example of Pure Radiation metric.