Software extensibility, the capability of adding new functions to a software system, is established based on software architecture. Therefore, developers need to evaluate the capability when designing software architecture. To support the evaluation, researchers have proposed metrics based on quality models or scenarios. However, those metrics are vague or subjective, depending on specific systems and evaluators. We propose the extensibility metric for software architecture (EMSA), which represents the degree of extensibility of a software system based on its architecture. To reduce the subjectivity of the metric, we first identify a typical task of adding new functions to a software system. Second, we define the metrics based on the characteristics of software architecture and its changes and finally combine them into a single metric. The originality of EMSA comes from defining metrics based on software architecture and extensibility tasks and integrating them into one. Furthermore, we made an effort to translate the degree into effort estimation expressed as person-hours. To evaluate EMSA, we conducted two types of user studies, obtaining measurements in both a laboratory and a real world project. The results show that the EMSA estimation is reasonably accurate [6.6% MMRE and 100% PRED(25%)], even in a real-world project (93.2% accuracy and 8.5% standard deviation).