Proficiency in units/dimensional analysis is a useful skill in the sciences and engineering, and STEM instructors often presume competence from their students in this area. However, unit analysis techniques and unit systems are not always formally taught, and even with explicit emphasis during instruction, many students lack the repeated exposure necessary to master them. To assess student understanding of units and unit systems, we administered a brief, itemized survey to N = 53 calculus-based introductory university physics students. The survey was intended to uncover possible misconceptions and identify previously unknown obstacles to student success within this topic. Our results suggest that as many as half of surveyed participants may not recognize the adaptability of symbolic physical equations to different unit systems. Furthermore, a similar proportion failed to eliminate non-viable answer choices involving analytic functions with units inside their arguments. Consequently, we believe units/dimensional analysis is a topic ripe for further investigation.