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Module coupling is an important criterion for evaluating the quality of a software design. While the benefits of reduced module coupling are widely agreed upon, it has been difficult to measure coupling and thus understand it empirically. This study argues the definition of coupling, defines a set of coupling metrics based on the measurement of connections of a module within its running environment, and validates the set using principal component analysis. In an empirical study, the results indicate that these coupling metrics capture three distinct attributes of module coupling. These three attributes represent sources of variation not accounted for in the set of metric primitives and are appropriate for evaluating the coupling complexity of software. This study provides a set of validated measurements of the coupling complexity of software and a new way to evaluate module coupling measurements.