The CO<sub>2</sub>-dependaency of stable carbon isotope fractionation (ε<sub>p</sub>) during marine algal carbon acquisition is widely used as a proxy for past atmospheric <em>p</em>CO<sub>2</sub>. However, a mechanistic model linking ε<sub>p</sub> and <em>p</em>CO<sub>2</sub> that explains observations in the modern ocean, culture experiments and across Pleistocene glacial-interglacial cycles is still lacking. Here, we present a multi-compartment model of an algal cell that simulates environmental control on passive CO<sub>2</sub> diffusion, active HCO<sub>3<sup><span>−</span></sup></sub> transport, and <sup>13</sup>C fractionation during C-fixation. Relative to previous models, our main new implementations include light-sensitive HCO<sub>3<sup><span>−</span></sup></sub> acquisition and calcification, and daylength-dependent pyrenoid permeability, based on physiological expectations. The model is fitted to and tested with culture data of multiple dinoflagellate species and the coccolithophore <em>Gephyrocapsa huxleyi</em>. This shows robust performance across a wide range of parameter values from culture experiments, implying an appropriate representation of the mechanistic control of <sup>13</sup>C-fractionation in algal organic matter, potentially paving the way for sedimentary work.