A measurement of the Drell-Yan fiducial cross section in the dimuon channel is presented differentially in terms of dimuon invariant mass, double differentially in terms of dimuon invariant mass and rapidity and double differentially in terms of dimuon invariant mass and muon separation . The cross sections are measured using 20:3 fb 1 of ATLAS data taken during 2012 at a centre of mass energy of ps = 8 TeV. Dedicated studies determining muon performance corrections for monte carlo isolation and trigger efficiencies and techniques for estimating backgrounds using data driven methods are described in detail. The fiducial cross sections agree within 10% of theoretical predictions in the regions where the statistical uncertainties are subdominant. Excluding the systematic uncertainty associated with the detector luminosity, a systematic uncertainty of below 2.5% is observed for the m < 300 GeV region for both the single and double differential cross section measurements. Theoretical predictions to NNLO in QCD including NLO higher order electroweak effects and a photon induced process component are found to underestimate the measurement by 3%. For the m < 300 GeV region the uncertainty of the measurement is smaller or of the same order as the theoretical predictions, which indicates that the results will provide useful information into the constraining and tuning of future physics models.