Amplified MRI (aMRI) is a promising new technique that can visualize pulsatile brain tissue motion by amplifying sub-voxel motion in cine MRI data, but it lacks the ability to quantify the sub-voxel motion field in physical units. Here, we introduce a novel post-processing algorithm called 3D quantitative amplified MRI (3D q-aMRI). This algorithm enables the visualization and quantification of pulsatile brain motion. 3D q-aMRI was validated and optimized on a 3D digital phantom and was applied in vivo on healthy volunteers for its ability to accurately measure brain parenchyma and CSF voxel displacement. Simulation results show that 3D q-aMRI can accurately quantify sub-voxel motions in the order of 0.01 of a voxel size. The algorithm hyperparameters were optimized and tested on in vivo data. The repeatability and reproducibility of 3D q-aMRI were shown on six healthy volunteers. The voxel displacement field extracted by 3D q-aMRI is highly correlated with the displacement measurements estimated by phase contrast (PC) MRI. In addition, the voxel displacement profile through the cerebral aqueduct resembled the CSF flow profile reported in previous literature. Differences in brain motion was observed in patients with dementia compared with age-matched healthy controls. In summary, 3D q-aMRI is a promising new technique that can both visualize and quantify pulsatile brain motion. Its ability to accurately quantify sub-voxel motion in physical units holds potential for the assessment of pulsatile brain motion as well as the indirect assessment of CSF homeostasis. While further research is warranted, 3D q-aMRI may provide important diagnostic information for neurological disorders such as Alzheimer's disease.