Here, we take advantage of the ability to sample genetically distinct coral colonies (genets) to produce genetically identical clonal fragments (ramets) and use an identical twin design to estimate the broad sense heritability (H2) and potential for adaptation of coral calcification rates under warming, acidification and the combination of both factors. Corals of eight species were exposed to one of four treatments: (i) control (present-day temperature and pH), (ii) ocean warming (+2°C and present-day pH), (iii) ocean acidification (present-day temperature and −0.2 pH units), or (iv) combined future ocean (+2°C and −0.2 pH units). This study was conducted over 1 year, providing the corals with time to acclimatize to the treatments and helping to ensure that the measured calcification responses were a result of heritable variation among them rather than differences in their short-term histories. This dataset is included in the OA-ICC data compilation maintained in the framework of the IAEA Ocean Acidification International Coordination Centre (see https://oa-icc.ipsl.fr). Original data were downloaded from Dryad (see Source) by the OA-ICC data curator. In order to allow full comparability with other ocean acidification data sets, the R package seacarb (Gattuso et al, 2024) was used to compute a complete and consistent set of carbonate system variables, as described by Nisumaa et al. (2010). In this dataset the original values were archived in addition with the recalculated parameters (see related PI). The date of carbonate chemistry calculation by seacarb is 2024-10-15.