In this work we compare an in-house designed Tangible User Interface (TUI) with three alternative single-user tools through an empirical investigation. These three alternative tools are a 3D physical, a 2D cardboard, and a mathematical tool. We expected the 3D physical to perform best, followed by the TUI, the 2D cardboard, and the mathematical tool. A pilot study was first carried out, the results of which were used to design a major experiment. Participants solved the same positioning problem, each using one of the four tools. The mathematical tool was not used in the experiment. In the experiment, trial time, number of user operations, learning effect in both preceding variables, and user satisfaction were measured. The 3D physical tool significantly outperformed the 2D cardboard tool. It also outperformed the TUI, but only in user satisfaction. This justifies the value of researching TUI systems and carrying out usability studies with such systems.