The perfectly linear temperature dependence of the electrical resistivity observed as T → 0 in a variety of metals close to a quantum critical point 1,2,3,4 is a major puzzle of condensed matter physics 5 . Here we show that T-linear resistivity as T → 0 is a generic property of cuprates, associated with a universal scattering rate. We measured the low-temperature resistivity of the bi-layer cuprate Bi2Sr2CaCu2O8+δ and found that it exhibits a T-linear dependence with the same slope as in the single-layer cuprates Bi2Sr2CuO6+δ (ref. 6), La1.6-xNd0.4SrxCuO4 (ref. 7) and La2-xSrxCuO4 (ref. 8), despite their very different Fermi surfaces and structural, superconducting and magnetic properties.We then show that the T-linear coefficient (per CuO2 plane), A1 ☐ , is given by the universal relation A1 ☐ TF = h / 2e 2 , where e is the electron charge, h is the Planck constant and TF is the Fermi temperature. This relation, obtained by assuming that the scattering rate 1 / τ of charge carriers reaches the Planckian limit 9,10 , whereby ħ / τ = kB T, works not only for hole-doped cuprates 6,7,8,11,12 but also for electrondoped cuprates 13,14 , despite the different nature of their quantum critical point and strength of their electron correlations.