Science and engineering heavily depend on the ability to share data and models. The World Wide Web provides even greater opportunity to reuse such information from disparate sources. Moreover, if the information is digitized it can to a large extent be processed automatically. However, information sharing requires the availability of proper formal standards. Ontologies provide such standards. Creating an ontology of units of measure is a crucial first step in unambiguously exchanging and processing quantitative information. The next step is to make this ontology available for software applications. In this paper we evaluate prevailing ontologies of units by comparing them to a semi-formal description of the domain of units of measure. This description was drafted from textual descriptions of standards in the field. An important result of the analysis is that existing ontologies only define subsets of the necessary concepts and relations identified in our reference description. We therefore propose a new ontology, called OM (Ontology of units of Measure and related concepts). The ontology is based on the description and the corresponding parts of the analyzed ontologies. OM defines the complete set of concepts in the domain as distinguished in the textual standards. As a result the ontology can answer a wider range of competency questions than the existing approaches do. Moreover, to make OM available for arbitrary software systems, we have developed a number of web services that offer a standardized interface. Three applications demonstrate the usefulness of OM and its services. First, a web application checks dimension and unit consistency of formulas. Second, an engineering application for agricultural supply chains computes product respiration quantities and measures. Third, a Microsoft Excel add-in assists in data annotation and unit conversion. Preliminary user evaluations indicate that OM and the associated services provide a useful component for software applications in science and engineering.