Hydraulic fracturing is a coupled multi-physics and scale-dependent process requiring an extensive numerical-laboratory appraisal to assess feasibility in the field. Developing a robust model of hydraulic fracture propagation requires knowledge of the time evolution of the fracture’s geometrical attributes, e.g., width/aperture and length/radius. However, it is inherently challenging to directly measure even the simplest fracture attribute (i.e., radius) within a rock sample subjected to in-situ stresses in the laboratory, let alone in the field. In this study, an analytical model is developed to predict the time evolution of the radius for a penny-shaped hydraulic fracture. This model (Rd) predicts the fracture opening and internal pressure gradient using Poiseuille’s law and assuming a self-similar propagation. Scaling laws and dimensional analysis are used to define propagation regimes; and non-linear hydro-mechanical coupling is accounted for in the near-tip region. We also quantify the growth of the fracture radius using linear elastic fracture growth model (RE); and tip asymptotic solutions (RV and RT). A comparison of the three analytical models with published experimental data reveal that (i) the asymptotic solutions are limited to linearly elastic and homogeneous materials, i.e., PMMA; (ii) the performance of the linear elastic model (RE) poorly matches the experimental data, especially for unstable propagation situations; (iii) the new Rd model takes advantage of a robust reconstruction of the temporal radius growth of hydraulic fracture problems under realistic stress conditions, and including multiscale propagation regimes, cohesive effects, as well as stable and unstable propagation regimes of geomaterials.