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The quantum definition based threshold voltage has been evaluated for triple-gate (TG) SOI FinFETs using self-consistent Schrodinger-Poisson solver. Although a new quantum definition of threshold voltage for multiple gate SOI MOSFETs has been provided in recent literature, in-depth analysis of quantization effects on threshold voltage calculation for highly scaled TG FinFETs is yet to be done. In this paper, the electrostatics of the device has been explored from a quantum mechanical point of view for variation in silicon film thickness in the sub 10 nm regime. Also the self-consistent solver, which takes wave function penetration and other quantum mechanical (QM) effects into account, has been utilized here to establish the capacitance-voltage (C-V) characteristics and a modified approach has been proposed for threshold voltage calculation.