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This paper introduces moral argument analytics, a technology that provides insights into the use of moral arguments in discourse. We analyse five socio-political corpora of argument annotated data from offline and online discussions, totalling 240k words with 9k arguments, with an average annotation accuracy of 78%. Using a lexicon-based method, we automatically annotate these arguments with moral foundations, achieving an estimated accuracy of 83%. Quantitative analysis allows us to observe statistical patterns and trends in the use of moral arguments, whereas qualitative analysis enables us to understand and explain the communication strategies in the use of moral arguments in different settings. For instance, supporting arguments often rely on Loyalty and Authority, while attacking arguments use Care. We find that online discussions exhibit a greater diversity of moral foundations and a higher negative valence of moral arguments. Online arguers often rely more on Harm rather than Care, Degradation rather than Sanctity. These insights have significant implications for AI applications, particularly in understanding and predicting human and machine moral behaviours. This work contributes to the construction of more convincing messages and the detection of harmful or biased AI-generated synthetic content. [ABSTRACT FROM AUTHOR]