Multiferroic BiFeO3 (BFO) that exhibits a gigantic off-centering polarization (OCP) is the most extensively studied material among all multiferroics. In addition to this gigantic OCP, the BFO having R3c structural symmetry is expected to exhibit a couple of parasitic improper polarizations owing to coexisting spin-polarization coupling mechanisms. However, these improper polarizations are not yet theoretically quantified. Herein, we show that there exist two distinct spin-coupling-induced improper polarizations in the R3c BFO on the basis of the Landau-Lifshitz-Ginzburg theory: ΔP LF arising from the Lifshitz gradient coupling in a cycloidal spin-density wave, and ΔP ms originating from the biquadratic magnetostrictive interaction. With the help of ab initio calculations, we have numerically evaluated magnitudes of these improper polarizations, in addition to the estimate of all three relevant coupling constants. We further predict that the magnetic susceptibility increases substantially upon the transition from the bulk R3c BFO to the homogeneous canted spin state in a constrained epitaxial film, which satisfactorily accounts for the experimental observation. The present study will help us understand the magnetoelectric coupling and shed light on design of BFO-based materials with improved multiferroic properties.