In this paper, we present MoiréTag—a novel tag-like device that magnifies displacement without active components for indirect sensing of subtle tangible interactions. The device consists of two overlapping layers of stripe patterns with distinct pattern frequencies. These layers create Moiré fringes that can move faster than the actual movement of a layer. Using a customized image processing pipeline, we show that MoiréTag can reliably detect sub-mm movement in real-time (mean error = 0.043 mm) under varying lighting conditions, camera angles, and camera distances. We also demonstrate five applications of MoiréTag to showcase its potential as a low-cost solution to capture and monitor small changes in movement and other physical properties, such as force and volume, by converting them into displacement.