We compute the moduli Kähler potential for M theory on a compact manifold of G2 holonomy in a large radius approximation. Our method relies on an explicit G2 structure with small torsion, its periods and the calculation of the approximate volume of the manifold. As a verification of our result, some of the components of the Kähler metric are computed directly by integration over harmonic forms. We also discuss the modification of our result in the presence of codimension-four singularities an...