This paper defines and calculates the Euler Sombor energy of a graph by summing the absolute values of the eigenvalues derived from its Euler Sombor matrix. This matrix, constructed based on vertex degrees, is linked to the Euler Sombor index. We establish mathematical properties for the Euler Sombor energy. Furthermore, we obtain bounds for this energy measure in graphs. Our analysis connects this new energy measure to other graph invariants, providing a comprehensive understanding of its characteristics and implications within the context of graph theory.