Measurements of differential cross sections d sigma/d phi* and double-differential cross sections d(2)sigma/ld phi*d/y/ for inclusive Z boson production are presented using the dielectron and dimuon final states. The kinematic observable phi* correlates with the dilepton transverse momentum but has better resolution, and y is the dilepton rapidity. The analysis is based on data collected with the CMS experiment at a centre-of-mass energy of 8 TeV corresponding to an integrated luminosity of 19.7 fb(-1). The normalised cross section (1/sigma) d sigma/d phi*, within the fiducial kinematic region, is measured with a precision of better than 0.5% for phi* < 1. The measurements are compared to theoretical predictions and they agree, typically, within few percent.