The variable-range hopping (VRH) model has been widely applied to describe low-temperature electrical transport in disordered systems. However, it relies on oversimplified approximations that restrict its applicability to rigid integer dimensions and narrow thermal windows, often resulting in problematic fitting behaviors and unphysical parameter extraction. In this work, we formulate an integral variable-range hopping (IVRH) model that replaces the traditional empirical temperature power laws with a physics-inspired integral formulation. The model builds upon the standard hopping rate $\omega (R)$ as a function of hopping distance $R$ and incorporates the density of accessible electronic states through a dimension-dependent hopping volume function $V(R)$, which naturally reflects the underlying system geometry. The IVRH formulation inherently captures both the low-temperature Mott VRH behavior and the high-temperature Arrhenius activation limit, enabling a seamless description of the crossover regime without manual temperature-window partitioning. We systematically apply the IVRH model to two-dimensional (2D), three-dimensional (3D), and multilayered systems. Monte Carlo simulations validate the model’s predictions and yield consistent, universal values for the geometric parameters, exhibiting substantially reduced variances compared with the standard VRH fits. Furthermore, the IVRH model outperforms traditional Mott-based power laws in trans-dimensional hafnium nitride (HfN) thin films and provides physically sound interpretations of carrier-density and gate-voltage-modulated localization physics in monolayer ${\mathrm{WS}}_2$ devices. Ultimately, the IVRH model offers a stable, precise, and unified framework for interpreting hopping transport in disordered, low-dimensional, and layered materials, providing deeper insights into the geometric scaling factors that govern charge transport.

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• Electrical conductivity
• Hopping transport
• Amorphous materials
• Disordered systems