What decisions do experts make when doing back-of-the-envelope calculations?

Back-of-the-envelope (BOTE) calculations require the use of estimations and approximations. They are used by expert physicists to simplify complex problems to obtain quick and approximate solutions. Though BOTE calculations are routine for experts in physics, they are not well defined in academic literature. In this study we interviewed 9 physicists working in academia and industry and characterized experts’ responses in terms of the decisions made during different stages of the solution process. These findings characterize the individual skills that students need to develop in order to solve BOTE problems. We find that BOTE calculations involve most of the same decisions as bigger research problems. Thus, BOTE problems represent authentic, real-world physics problems that present challenges undergraduate students are often not prepared to solve. This provides an interesting foundation for future work characterizing other factors that influence both students’ and experts’ decisions to perform BOTE calculations.