Granularity is an integral feature of both anchored (e.g., 25 October 1995; July 1996) and unanchored (e.g., 3 minutes, 6 hours 20 minutes, 5 days, 1 week) temporal data. In supporting temporal data that is specified in different granularities, numerous approaches have been proposed to deal with the issues of converting temporal data from one granularity to another. The emphasis, however, has only been on granularity conversions with respect to anchored temporal data. This is because a granularity in these approaches is modeled as an anchored partitioning of the time axis, thereby making it difficult to deal with granularity conversions in unanchored temporal data. In this paper we provide a novel approach to the treatment of granularity in temporal data. A granularity is modeled as a special kind of unanchored temporal primitive that can be used as a unit of time. That is, a granularity is modeled as a unit unanchored temporal primitive. Granularities are accommodated within the context of calendars and granularity conversions are presented and discussed in terms of unanchored durations of time. This allows us to consistently model and operate on unanchored temporal data that is comprised of different and mixed granularities. Specifically, we show how unanchored temporal data is represented, give procedures for converting the data to a given granularity, provide canonical forms for the data, and describe how operations between the data are performed.