This paper proposes an interactive rear-projection tabletop glasses-free 3D display using a novel wireless magnetic motion capture system. Our tracking system employs an electromagnetic field generator and 16 magnetic detectors. It detects the 3D positions of several small markers in the generated electromagnetic field. The detectors are arranged in a ring around the rim of the conical screen of the 3D display to avoid occluding the reproduced 360-degree-viewable 3D images. For the proposed configuration, our experimental results reveal that a toroidal area around a hemispherical 3D image display area allows the 3D position to be measured with sufficient accuracy. We implemented an application to demonstrate real-time interaction with virtual 3D objects displayed on the table using markers attached to a physical object like a stick or finger.