Photon-diffusion theory has had limited success in modeling the optical transmittance of whole blood. Therefore we have developed a new photon-diffusion model of the optical absorbance of blood. The model has benefited from experiments designed to test its fundamental assumptions, and it has been compared extensively with transmittance data from whole blood. The model is consistent with both experimental and theoretical notions. Furthermore, when all parameters associated with a given optical geometry are known, the model needs no variational parameters to predict the absolute transmittance of whole blood. However, even if the exact value of the incident light intensity is unknown (which is the case in many situations), only a single additive constant is required to scale experiment to theory. Finally, the model is shown to be useful for simulating scattering effects and for delineating the relative contributions of the diffuse transmittance and the collimated transmittance to the total optical density of whole blood. Applications of the model include oximetry and measurements of the arteriovenous oxygen difference in whole, undiluted blood.