Abstract: Interpolation is a method of constructing new data point within the range of a discrete set of known data points. Different methods have been developed to construct useful interpolation formulae, for evenly as well as unevenly spaced data points. This paper is aimed at developing a central difference interpolation formula which is derived from Gauss’s Backward Formula and another formula in which we retreated the subscript in Gauss’s Forward Formula by two units and replacing u by u+2.