Units of measure are critical in many scientific fields. While instructors often note that students struggle with units, little research has been conducted about the nature and extent of these difficulties or why they exist. We investigated calculus students' unit use in area and volume computations. Seventy-three percent of students gave incorrect units for at least one task. The most common error was the misappropriation of length units in area and volume computations. Analyses of interview data indicate that some students think that the unit of the computation should be the same as the unit specified in the task statement. Findings also suggest that some students have difficulties correctly indicating the units for computations that involve the quantity "p." We discuss students' correct and incorrect use of unit in relation to their understanding of area and volume as arrays, as well as in terms of Sherin's Symbolic Forms.