We introduce the constants E[t,X], CNJ[X] and J[t,X] to describe the asymmetry of the norm. They can be seen as the skew version of the Gao's parameter, von Neumann-Jordan constant and Milman's moduli, respectively. We establish basic properties of these constants, relating them other well known constants, and use these properties to calculate the constants for specific spaces. We then use these constants to study Hilbert spaces, uniformly non-square spaces and their normal structures. With the Banach-–Mazur distance, we use them to study isomorphic Banach spaces.

Keywords: geometric constant, uniform non-squareness, normal structure