Understanding the privacy relevant characteristics of data sets, such as reidentifiability and joinability, is crucial for data governance, yet can be difficult for large data sets. While computing the data characteristics by brute force is straightforward, the scale of systems and data collected by large organizations demands an efficient approach. We present KHyperLogLog (KHLL), an algorithm based on approximate counting techniques that can estimate the reidentifiability and joinability risks of very large databases using linear runtime and minimal memory. KHLL enables one to measure reidentifiability of data quantitatively, rather than based on expert judgement or manual reviews. Meanwhile, joinability analysis using KHLL helps ensure the separation of pseudonymous and identified data sets. We describe how organizations can use KHLL to improve protection of user privacy. The efficiency of KHLL allows one to schedule periodic analyses that detect any deviations from the expected risks over time as a regression test for privacy. We validate the performance and accuracy of KHLL through experiments using proprietary and publicly available data sets.