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Osteoporosis is a disease characterized by a degradation of bone structures. Various methods have been developed to diagnose osteoporosis by measuring bone mineral density (BMD) of patients. However, BMDs from these methods were not equivalent and were incomparable. In addition, partial volume effect introduces errors in estimating bone volume from computed tomography (CT) images using image segmentation. In this study, a two-compartment model (TCM) was proposed to calculate bone volume fraction (BV/TV) and BMD from CT images. The TCM considers bones to be composed of two sub-materials. Various equivalent BV/TV and BMD can be calculated by applying corresponding sub-material pairs in the TCM. In contrast to image segmentation, the TCM prevented the influence of the partial volume effect by calculating the volume percentage of sub-material in each image voxel. Validations of the TCM were performed using bone-equivalent uniform phantoms, a 3D-printed trabecular-structural phantom, a temporal bone flap, and abdominal CT images. By using the TCM, the calculated BV/TVs of the uniform phantoms were within percent errors of ±2%; the percent errors of the structural volumes with various CT slice thickness were below 9%; the volume of the temporal bone flap was close to that from micro-CT images with a percent error of 4.1%. No significant difference (p >0.01) was found between the areal BMD of lumbar vertebrae calculated using the TCM and measured using dual-energy X-ray absorptiometry. In conclusion, the proposed TCM could be applied to diagnose osteoporosis, while providing a basis for comparing various measurement methods. [ABSTRACT FROM PUBLISHER]