A business process is a set of structured, related activities that aims at fulfilling a specific organizational goal for a customer or market. An important metric when developing a business process is its degree of parallelism, i.e., the maximum number of tasks that are executable in parallel in that process. The degree of parallelism determines the peak demand on tasks, providing a valuable guide for the problem of resource allocation in business processes. In this paper, we investigate how to automatically measure the degree of parallelism for business processes, described using the BPMN standard notation. We first present a formal model for BPMN processes in terms of Labelled Transition Systems, which are obtained through process algebra encodings. We then propose an approach for automatically computing the degree of parallelism by using model checking techniques and dichotomic search. We implemented a tool for automating this check and we applied it successfully to more than one hundred BPMN processes.