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[Formula: see text] at [Formula: see text] = 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 [Formula: see text] contact interaction scale [Formula: see text] between 15.4 TeV and 26.3 TeV, at the 95 % credibility level. For large extra spatial dimensions, lower limits are set on the string scale [Formula: see text] between 3.2 TeV to 5.0 TeV.