The paper, first of all, contains a theoretical analysis of the relationship between law and morality as the two most important regulators of social relations is carried out. An analysis is given of both natural law and positivist approaches to the relationship between law and morality in the works of domestic and foreign legal scholars. According to the authors, despite the long history of the formation of relevant theoretical concepts, the development of a structured idea of the relationship between ethics and law in various areas of social relations remains relevant. Both the basic model of the relationship between the two regulatory systems and special models of their relationship and mutual influence in specific areas of society, which determine the fairness and effectiveness of regulation in the context of conjugation of ethics, law, economic and social development, need to be defined. The practical result of the development of such a model is the creation of an index of ethicality of the law, and related indicators. The index of ethicality of the law is a digital product, a machine algorithm built on the principles of learning neural networks. The article describes the phases and content of the work on creating the index as part of the HSE research project, and draws attention to the theory of moral foundations, which forms the basis for the development of related tools. Comparison of the norms of legal acts or their drafts with moral norms and principles relevant to society, of course, requires a reliable picture of the content of the latter. The identification, by means of sociological methods, of the content of moral grounds as the basic criteria for the moral assessment of human behavior will make it possible to compare the ethical ideas of modern Russian society with the content of legal norms that have an ethical load. The index as product can be equally useful both in the legal regulation of social relations through the adoption of legal acts, and in their interpretation and application (including judicial). The authors are convinced that the formation of a social, industrial, cultural and business environment in which it would be comfortable for a person to live, work and pass on his life experience to a new generation requires a systematic reconciliation and correlation with each other of the two systems of social regulation. Such reconciliation can be carried out, among other things, with the help of the latest technologies available to mankind.