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This paper presents a study on the relationship between transport properties and geometric free volume for a hard sphere (HS) system in a dense fluid region. First, a generic free volume distribution function is proposed based on recent simulation results on the HS geometric free volume by Maiti and Sastry [J. Chem. Phys. 141(4), 044510 (2014)] and Maiti et al. [Eur. Phys. J. E 36(1), 5 (2013)]. Combining the new distribution function with a local particle transportation model, we obtain a power law for the HS transport properties. Then, a relation between the geometric free volume and thermodynamic free volume is established, which makes it possible to use well-developed equations of state (EoS) for the expressions of the geometric free volume. The new power law models are tested with molecular dynamic simulation results for HS viscosity, diffusivity and thermal conductivity, respectively, and the results are very satisfactory. Moreover, using the power law, we are able to reproduce several equations obtained from different approaches, such as the entropy scaling laws [Bell et al., J. Phys. Chem. B 123(29), 6345–6363 (2019]), mode coupling theory [Barrat et al., J. Phys. Condens. Matter 1, 7163–7170 (1989)], or empirical correlations [Sigurgeirsson and Heyes, J. Mol. Phys. 101(3), 469–482 (2003)]. In particular, a long-standing controversy regarding the well-known Cohen–Turnbull–Doolittle free volume model [Cohen and Turnbull, J. Chem. Phys. 31(3), 1164–1169 (1959); Doolittle, J. Appl. Phys. 22(12), 1471–1475 (1951)] is resolved by using the power law combined with the Heyes and Woodcock EoS [Heyes and Woodcock, Mol. Phys. 59(6), 1369–1388 (1986)]. [ABSTRACT FROM AUTHOR]