Computationally inexpensive carbon cycle models serve as critical and efficient tools for illuminating the complex dynamics of the carbon cycle and its interplay with the climate system, offering insights into how our planet has responded to climate perturbations throughout its history. During geologic hyperthermal events, carbon cycle models are employed to trace the trajectory of carbon emissions and establish a connection between the emission trajectory and changes in the Earth's surface environment. To date, the prevalent method to estimate the carbon emission rate relies on coupling the carbon cycle modeling and proxy reconstructions. Most previous studies employ a forward methodology, i.e., they force the model with an array of predefined carbon injection scenarios and select the one that produces the best fit to one or more specific proxy-derived records (e.g., atmospheric pCO2, sea surface pH, and calcite compensation depth) as the optimal solution. However, this forward method has two potential disadvantages. First, it can be computationally expensive, particularly when tens of thousands of scenarios need to be conducted to find the best solution. Second, it might not yield the best injection trajectory if none of the predefined carbon emission curves represents the realistic emission curve. Hence, an inverse model that can reconstruct the carbon emission trajectory directly from the record/records is urgently needed. In this study, building upon the Long-term Ocean-atmosphere-Sediment CArbon cycle Reservoir (LOSCAR) Model (Zeebe, 2012), we develop an interactive carbon cycle model (named iLOSCAR) using the open-source Python language and include two options, a forward model and an inverse model. The forward model replicates the original LOSCAR model, while the inverse model calculates the emission trajectory constrained by the proxy records in a single run. Both models are accessible via a web-based interface, which allows users to interactively tune model parameters and conduct experiments. In this paper, we present the details of iLOSCAR, including model structure and derivation of key equations. We then validate iLOSCAR's performance through an identical twin test and model intercomparison. We also apply it to a climatic perturbation event to diagnose features of the emission pattern that were overlooked in previous studies. Finally, we discuss the possible directions for model's future development.