Based on the cross-correlation analysis of the Kikuchi diffraction patterns, high-resolution electron backscatter diffraction (HR-EBSD) is a well established method for determining internal stress in the deformed crystalline materials. In many cases, however, the stress values evaluated at different sampling points have a large scatter of the order of GPa. As demonstrated by Wilkinson et al. [Appl. Phys. Lett. 105, 181907 (2014)], this is due to the long tail of the probability distribution (P(sigma)) of the eigen-stress generated by the dislocations present in the system. According to the theoretical investigations of Groma and Bako [Phys. Rev. B 58, 2969 (1998)], the tail of P(sigma) is inverse cubic with a prefactor proportional to the total dislocation density hqi. This paper presents the details of determination from P(sigma) contributing to the proper physical understanding of the method. The values determined on the deformed Cu single crystals show good agreement with the results of X-ray line profile analysis, granting credibility to the EBSD approach. The availability of spatially resolved stress maps opens further perspectives for the evaluation of correlation properties and mesoscale parameters of heterogeneous dislocation structures. Published by AIP Publishing.