Additive manufacturing techniques are revolutionizing product development by enabling fast turnaround from design to fabrication. However, the throughput of the rapid prototyping pipeline remains constrained by print optimization, requiring multiple iterations of fabrication and ex-situ metrology. Despite the need for a suitable technology, robust in-situ shape measurement of an entire print is not currently available with any additive manufacturing modality. Here, we address this shortcoming by demonstrating fully simultaneous 3D metrology and printing. We exploit the dramatic increase in light scattering by a photoresin during gelation for real-time 3D imaging of prints during tomographic volumetric additive manufacturing. Tomographic imaging of the light scattering density in the build volume yields quantitative, artifact-free 3D + time models of cured objects that are accurate to below 1% of the size of the print. By integrating shape measurement into the printing process, our work paves the way for next-generation rapid prototyping with real-time defect detection and correction.