Fermatean fuzzy set is a competent tool in curbing indeterminacy embedded in soft computing. Fermatean fuzzy set generalizes both intuitionistic fuzzy sets and Pythagorean fuzzy sets in an effective way to handle imprecision by expanding the spatial scope of Pythagorean/intuitionistic fuzzy sets. Distance measure has become an integral aspect of utilizing generalized fuzzy sets in soft computing. In this paper, a novel distance measure between Fermatean fuzzy sets is introduced with a better and reliable output. Some properties of the proposed distance measure are characterized. It is demonstrated that the new distance measure between Fermatean fuzzy sets is more reliable than the existing Fermatean fuzzy distance measure. In addition, it is shown that Fermatean fuzzy set is more equipped to curb imprecision than Pythagorean/intuitionistic fuzzy sets. In terms of application, the new Fermatean fuzzy distance measure is utilized in executing students’ admission process using an algorithmic approach implemented by a programming language to enhance accuracy and ease of computations.