Using data recorded in 2011 with the ATLAS detector at the Large Hadron Collider, a search for evidence of extra spatial dimensions has been performed through an analysis of the diphoton final state. The analysis uses data corresponding to an integrated luminosity of 2.12 fb-1 of √s = 7 TeV proton– proton collisions. The diphoton invariant mass (mγγ) spectrum is observed to be in good agreement with the expected Standard Model background. In the large extra dimension scenario of Arkani-Hamed, Dimopoulos and Dvali, the results provide 95% CL lower limits on the fundamental Planck scale between 2.27 and 3.53 TeV, depending on the number of extra dimensions and the theoretical formalism used. The results also set 95% CL lower limits on the lightest Randall–Sundrum graviton mass of between 0.79 and 1.85 TeV, for values of the dimensionless coupling k/MPl varying from 0.01 to 0.1. Combining with previously published ATLAS results from the dielectron and dimuon final states, the 95% CL lower limit on the Randall–Sundrum graviton mass for k/MPl = 0.01 (0.1) is 0.80 (1.95) TeV.