Coccolithophores are the most abundant calcifying phytoplankton in the ocean. These tiny primary producers have an important role in the global carbon cycle, substantially contributing to global ocean calcification, ballasting organic matter to the deep sea, forming part of the marine food web base, and influencing ocean-atmosphere CO2 exchange. Despite these important impacts, coccolithophores are not explicitly simulated in most marine ecosystem models and, therefore, their impacts on carbon cycling are not represented in most Earth system models. Here, we compile field and laboratory data to synthesize overarching, across-species relationships between environmental conditions and coccolithophore growth rates and relative calcification (reported as a ratio of particulate inorganic carbon to particulate organic carbon in coccolithophore biomass, PIC/POC). We apply our relationships in a generalized coccolithophore model, estimating current surface ocean coccolithophore growth rates and relative calcification, and projecting how these may change over the 21st century using output from the Community Earth System Model large ensemble. We find that average increases in sea surface temperature of ∼2–3 °C lead to faster coccolithophore growth rates globally (>10% increase) and increased calcification at high latitudes. Roughly an ubiquitous doubling of surface ocean pCO2 by the end of the century has the potential to moderately stimulate coccolithophore growth rates, but leads to reduced calcification (∼25% decrease). Decreasing nutrient availability (from warming-induced increases in stratification) produces increases in relative calcification, but leads to ∼25% slower growth rates. With all drivers combined, we observe decreases in calcification and growth in most low and mid latitude regions, with possible increases in both of these responses in most high latitude regions. Major limitations of our coccolithophore model stem from a lack of conclusive physiological responses to changes in irradiance (we do not include light limitation in our model), and a lack of physiological data for major coccolithophore species. Species within the Umbellosphaera genus, for example, are dominant in mid to low latitude regions where we predict some of the largest decreases in coccolithophore growth rate and calcification.