The inner core’s axial torsional libration (ATL) is a manifestation of the mantle-inner core gravitational (MICG) rotational normal mode. Its natural period is critically determined by the interior sectoral quadrupole of (of mass distribution of spherical-harmonic degree 2 and order 2) belonging to the mantle plus the core-mantle boundary. We derive the (multipole) formalism to calculate of based on two physical postulations: (i) Postulation I that equates the observed 6-year variation in Earth’s length-of-day to ATL as laid out in Chao (2017); (ii) Postulation II requiring that the shape of IC, thanks to its finite viscosity, conforms to the gravitational equi-potential surface in the long term as proposed by Buffett (1997). of being a complex value, its phase relation with ATL asserts that the major axis of the IC aligns with that of of subject to the lowest-energy state. The magnitude of of thus evaluated by Earth parameters is about 0.78 – 1.71 kg m, with the two endmember values corresponding respectively to IC’s nominal polar moment of inertia vs. the effective value under 100% tangent-cylinder coupling. The corresponding equatorial elliptical shape of the IC under Postulation II has peak-to-peak topography of 75 – 164 m. The acquired of can serve as source information for inversion on, among others, the density anomaly of the LLSVP (large low shear velocity provinces) constructs in the lower mantle.