Data quality is a serious concern in every data management application, and a variety of quality measures have been proposed, e.g., accuracy, freshness and completeness, to capture common sources of data quality degradation. We identify and focus attention on a novel measure, column heterogeneity, that seeks to quantify the data quality problems that can arise when merging data from different sources. We identify desiderata that a column heterogeneity measure should intuitively satisfy, and describe our technique to quantify database column heterogeneity based on using a novel combination of cluster entropy and soft clustering. Finally, we present detailed experimental results, using diverse data sets of different types, to demonstrate that our approach provides a robust mechanism for identifying and quantifying database column heterogeneity.