Privacy protection technology is an important guarantee to prevent the privacy disclosure of sensitive information in the cloud computing environment. In order to design better privacy protection schemes, a privacy measurement technique is required that can reflect the privacy protection intensity by measuring the disclosure risk of privacy information in the privacy protection schemes. Therefore, privacy measurement is of great significance for the privacy protection of the cloud data. This paper systematically reviews the existing methods of privacy measurement for the cloud data. Firstly, an overview of the privacy protection and privacy measurement is provided along with descriptions of some quantitative methods of the background knowledge for the attacks, some performance evaluation indexes and a comprehensive evaluation framework of the privacy protection schemes for the cloud data. Moreover, an abstract model of the privacy measurement for the cloud data is proposed, and the existing privacy measurement methods are elaborated based on anonymity, information entropy, set pair analysis theory and differential privacy respectively from the perspective of working principle and the specific implementation. Furthermore, the advantages and disadvantages and the application scopes of the above four types of privacy measurement methods are analyzed by the privacy measurement indexes and effectiveness. Finally, the development trends and the future problems of the privacy measurement for the cloud data are summarized in terms of the privacy measurement processes, effects and methods.