The Open Biomedical Ontology (OBO) format emerged from the Gene Ontology, and now supports many other important ontologies. If we compare OBO to OWL, the ontology language of the Semantic Web, the latter anticipates integral query languages, rule languages and distributed infrastructure for information interchange. A convenient method for leveraging these other features for OBO ontologies is by transforming OBO ontologies to OWL. We have developed a methodology for translating OBO ontologies to OWL using the organization of the Semantic Web layer cake to guide the work. The approach reveals that the constructs of OBO can be grouped together to form a similar layer cake. Thus we were able to identify the constructs of OBO that have easy semantic equivalence to a construct in the OWL stack, and as well as those constructs that entail the challenges to a transformation system. As a result, we have developed a standard common mapping between OBO and OWL for the OBO community. Our mapping produces OWL-DL a Description Logics based dialect of OWL with desirable computational properties for efficiency and correctness. Our Java implementation of the mapping is part of the official Gene Ontology project source. Our transformation system provides a lossless roundtrip mapping for OBO ontologies, i.e. an OBO ontology may be translated to OWL and back without loss of knowledge.