This paper raises concerns about the energy consumption and environmental impact of generative AI, especially large-scale language models (LLMs), and emphasizes the importance of energy consumption estimation in establishing sustainability strategies. We point out the shortcomings of existing energy consumption monitoring and estimation tools (high input data requirements, invasive nature, high error rates, etc.) and aim to address these issues by leveraging the latest LLM benchmark data. In this paper, we present R-ICE, a novel framework for estimating prompted-level inference carbon emissions, and present promising validation results demonstrating the potential of benchmark-based modeling. R-ICE provides a practical and non-invasive method that enables new use cases such as dynamic LLM routing and carbon accounting.