Increased usage of generative AI (GenAI) in Human-Computer Interaction (HCI) research induces a climate impact from carbon emissions due to energy consumption of the hardware used to develop and run GenAI models and systems. The exact energy usage and and subsequent carbon emissions are difficult to estimate in HCI research because HCI researchers most often use cloud-based services where the hardware and its energy consumption are hidden from plain view. The HCI GenAI CO2ST Calculator is a tool designed specifically for the HCI research pipeline, to help researchers estimate the energy consumption and carbon footprint of using generative AI in their research, either a priori (allowing for mitigation strategies or experimental redesign) or post hoc (allowing for transparent documentation of carbon footprint in written reports of the research).