In this Perspective, a mistake was identified in the description of the example provided in Box 2. The sentence “It is derived as the average over four observational datasets60,106–110 (0.87 °C), corrected for by the ratio between surface air temperature and blended temperatures (surface air temperature over land and sea-ice regions combined with sea surface temperature over open ocean) informed by models.” has been replaced by “It is derived by correcting the estimate of a global dataset60,106 using the ratio between global surface air temperature and blended temperatures (surface air temperature over land and sea-ice regions combined with sea surface temperature over open ocean) based on incomplete geographical coverage, as informed by models.”. This means that original references 107–110 (Cowtan, K. & Way, R. G. Q. J. R. Meteorol. Soc. 140, 1935–1944 (2014); Vose, R. S. et al. Bull. Am. Meteorol. Soc. 93, 1677–1685 (2012); Karl, T. R. et al. Science 348, 1469–1472 (2015); and Hansen, J., Ruedy, R., Sato, M. & Lo, K. Rev. Geophys. 48, RG4004 (2010)) have been deleted because they are no longer cited. Furthermore, in Supplementary Tables 1 and 2 of this Perspective, the legend now refers to Fig. 2 instead of the non-existent Fig. 3 in the text “Estimates are listed in the same order as shown in Figure 2 in the main paper”, and “until 2015” has been replaced by “until 2006–2015” in the ‘Historical human-induced warming’ column of the rows numbered 1 to 4. To clarify how values in Box 2 combine to provide the reported remaining carbon budget estimates, we additionally report tabulated unrounded values of the various terms that, after adequate insertion into equation (1), adjusting for estimated 289.8 Gt CO 2 of historical CO 2 emissions between 2011 and 2017, and rounding to the nearest 10, result in the values reported in Box 2 (see the Supplementary Information to this Amendment). We thank Dave Clarke for identifying and reporting these issues. These corrections have no further implications for the findings, conclusions or discussion presented in the Perspective. The original Perspective has been corrected online.