We discuss three measures of the degree of contextuality in contextual systems of dichotomous random variables. These measures are developed within the framework of the Contextuality-by-Default (CbD) theory, and apply to inconsistently connected systems (those with ‘disturbance’ allowed). For one of these measures of contextuality, presented here for the first time, we construct a corresponding measure of the degree of non-contextuality in non-contextual systems. The other two CbD-based measures do not suggest ways in which degree of non-contextuality of a non-contextual system can be quantified. We find the same to be true for the contextual fraction measure developed by Abramsky, Barbosa and Mansfield. This measure of contextuality is confined to consistently connected systems, but CbD allows one to generalize it to arbitrary systems.This article is part of the theme issue ‘Contextuality and probability in quantum mechanics and beyond’.