The ability to accurately map the 3D geometry of single-molecule complexes in trace samples is a challenging goal that would lead to new insights into molecular mechanics and provide an approach for single-molecule structural proteomics. To enable this, we have developed a high-resolution force spectroscopy method capable of measuring multiple distances between labeled sites in natively folded protein complexes. Our approach combines reconfigurable nanoscale devices, we call DNA nanoswitch calipers, with a force-based barcoding system to distinguish each measurement location. We demonstrate our approach by reconstructing the tetrahedral geometry of biotin-binding sites in natively folded streptavidin, with 1.5-2.5 Å agreement with previously reported structures.