Quantitative 2D neutron dark-field-imaging with neutron grating interferometry has been used to characterize structures in the size range below the imaging resolution. We present the first 3D quantitative neutron dark-field imaging experiment. We characterize sub-pixel structure sizes below the imaging resolution in tomography by quantitatively analyzing the change in dark-field contrast with varying neutron wavelength. This proof of principle experiment uses a dedicated reference sample with four different solutions of microspheres, each with a different diameter. The result is a 3D tomogram featuring a real space scattering function in each voxel. The presented experiment is expected to mark the path for future material science research through the individual quantification of small-angle scattering structures in each voxel of a volume of a bulk inhomogeneous sample material.