  We calculate the carrier density dependent ground state properties of
graphene in the presence of random charged impurities in the substrate taking
into account disorder and interaction effects non-perturbatively on an equal
footing in a self-consistent theoretical formalism. We provide detailed
quantitative results on the dependence of the disorder-induced spatially
inhomogeneous two-dimensional carrier density distribution on the external gate
bias, the impurity density, and the impurity location. We find that the
interplay between disorder and interaction is strong, particularly at lower
impurity densities. We show that for the currently available typical graphene
samples, inhomogeneity dominates graphene physics at low ($\lesssim 10^{12}$
cm$^{-2}$) carrier density with the density fluctuations becoming larger than
the average density.
