Measurements of differential cross sections dσ/dϕ* and double-differential cross sections d2σ/dϕ*d|y| for inclusive Z boson production are presented using the dielectron and dimuon final states. The kinematic observable ϕ* 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/σ) dσ/dϕ*, within the fiducial kinematic region, is measured with a precision of better than 0.5% for ϕ* < 1. The measurements are compared to theoretical predictions and they agree, typically, within few percent.