We construct a carbon cycle box model to process observed or inferred geochemical evidence from modern and paleo settings. The [simple carbon project] model v1.0 (SCP-M) combines a modern understanding of the ocean circulation regime with the Earth's carbon cycle. SCP-M estimates the concentrations of a range of elements within the carbon cycle by simulating ocean circulation, biological, chemical, atmospheric and terrestrial carbon cycle processes. The model is capable of reproducing both paleo and modern observations and aligns with CMIP5 model projections. SCP-M's fast run time, simplified layout and matrix structure render it a flexible and easy-to-use tool for paleo and modern carbon cycle simulations. The ease of data integration also enables model-data optimisations. Limitations of the model include the prescription of many fluxes and an ocean-basin-averaged topology, which may not be applicable to more detailed simulations. In this paper we demonstrate SCP-M's application primarily with an analysis of the carbon cycle transition from the Last Glacial Maximum (LGM) to the Holocene and also with the modern carbon cycle under the influence of anthropogenic CO2 emissions. We conduct an atmospheric and ocean multi-proxy model-data parameter optimisation for the LGM and late Holocene periods using the growing pool of published paleo atmosphere and ocean data for CO2, delta C-13, Delta C-14 and the carbonate ion proxy. The results provide strong evidence for an ocean-wide physical mechanism to deliver the LGM-to-Holocene carbon cycle transition. Alongside ancillary changes in ocean temperature, volume, salinity, sea-ice cover and atmospheric radiocarbon production rate, changes in global overturning circulation and, to a lesser extent, Atlantic meridional overturning circulation can drive the observed LGM and late Holocene signals in atmospheric CO2, delta C-13, Delta C-14, and the oceanic distribution of delta C-13, Delta C-14 and the carbonate ion proxy. Further work is needed on the analysis and processing of ocean proxy data to improve confidence in these modelling results.