We have proposed an approach for converting the reduced molecular scattering curves (sM(s)) from the reciprocal space (s-space) into the real space (r-space) radial distribution functions (RDF) using the regularized weighted sine least-squares spectral analysis (rwsLSSA). Our method directly maps the experimentally measured scattering pattern with uncertainties in the s-space into the pair of RDF values with their uncertainties in the r-space. The performance of this approach was demonstrated with numerical examples.