The widespread adoption of Electronic Health Records (EHRs) and large-scale clinical databases has significantly advanced medical research, yet it introduces substantial privacy risks when sharing sensitive patient information. While various privacy-preserving techniques and models exist, evaluating the actual level of protection achieved in complex healthcare datasets, such as those following the OMOP CDM, remains a significant challenge. This paper proposes DataPrivScore, a serverless web application designed to quantify privacy risks through a comprehensive metric called the Privacy Index. The framework locally processes datasets within the user's browser to ensure data residency and security. It utilizes a tiered, automated attribute classification system, supported by a manual override to classify attributes. Experimental results using synthetic datasets in standard formats demonstrate the tool's effectiveness in distinguishing between varying degrees of data protection and identifying critical vulnerabilities in healthcare data. The tool is open-source, and the code is publicly available at https://github.com/ieeta-mith/DataPrivScore.