The ATLAS inner detector comprises three different sub-detectors: the pixel detector, the silicon strip tracker, and the transition-radiation drift-tube tracker. The Insertable B-Layer, a new innermost pixel layer, was installed during the shutdown period in 2014, together with modifications to the layout of the cables and support structures of the existing pixel detector. The material in the inner detector is studied with several methods, using a low-luminosity root s = 13 TeV pp collision sample corresponding to around 2.0 nb(-1) collected in 2015 with the ATLAS experiment at the LHC. In this paper, the material within the innermost barrel region is studied using reconstructed hadronic interaction and photon conversion vertices. For the forward rapidity region, the material is probed by a measurement of the efficiency with which single tracks reconstructed from pixel detector hits alone can be extended with hits on the track in the strip layers. The results of these studies have been taken into account in an improved description of the material in the ATLAS inner detector simulation, resulting in a reduction in the uncertainties associated with the charged-particle reconstruction efficiency determined from simulation.