A search is conducted for non-resonant new phenomena in dielectron and dimuon final states, originating from either contact interactions or large extra spatial dimensions. The LHC 2012 proton-proton collision dataset recorded by the ATLAS detector is used, corresponding to 20 fb(-1) at root s = 8 TeV. The dilepton invariant mass spectrum is a discriminating variable in both searches, with the contact interaction search additionally utilizing the dilepton forward-backward asymmetry. No significant deviations from the Standard Model expectation are observed. Lower limits are set on the llqq contact interaction scale Lambda between 15.4 TeVand 26.3 TeV, at the 95\% credibility level. For large extra spatial dimensions, lower limits are set on the string scale MS between 3.2 TeV to 5.0 TeV.