The luminosity calibration for the ATLAS detector at the LHC during pp collisions at √s = 7 TeV in 2010 and 2011 is presented. Evaluation of the luminosity scale is performed using several luminosity-sensitive detectors, and comparisons are made of the long-term stability and accuracy of this calibration applied to the pp collisions at √s = 7 TeV. A luminosity uncertainty of δL/L=±3.5 % is obtained for the 47 pb−1 of data delivered to ATLAS in 2010, and an uncertainty of δL/L=±1.8 % is obtained for the 5.5 fb−1 delivered in 2011.