Abstract The luminosity determination for the ATLAS detector at the LHC during Run 2 is presented, with pp collisions at a centre-of-mass energy $$\sqrt{s}=13$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msqrt> <mml:mi>s</mml:mi> </mml:msqrt> <mml:mo>=</mml:mo> <mml:mn>13</mml:mn> </mml:mrow> </mml:math> TeV. The absolute luminosity scale is determined using van der Meer beam separation scans during dedicated running periods in each year, and extrapolated to the physics data-taking regime using complementary measurements from several luminosity-sensitive detectors. The total uncertainties in the integrated luminosity for each individual year of data-taking range from 0.9% to 1.1%, and are partially correlated between years. After standard data-quality selections, the full Run 2 pp data sample corresponds to an integrated luminosity of $$140.1\pm 1.2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>140.1</mml:mn> <mml:mo>±</mml:mo> <mml:mn>1.2</mml:mn> </mml:mrow> </mml:math> $$\hbox {fb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>fb</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> , i.e. an uncertainty of 0.83%. A dedicated sample of low-pileup data recorded in 2017–2018 for precision Standard Model physics measurements is analysed separately, and has an integrated luminosity of $$338.1\pm 3.1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>338.1</mml:mn> <mml:mo>±</mml:mo> <mml:mn>3.1</mml:mn> </mml:mrow> </mml:math> $$\hbox {pb}^{-1}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mtext>pb</mml:mtext> <mml:mrow> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msup> </mml:math> .