Artificial Intelligence (AI) coupled with the existing Internet of Things (IoT) enables more autonomous operations across various economic sectors. While this paradigm shift results in increased energy consumption it is difficult to quantify the end-to-end energy consumption of such systems with the conventional metrics as they either focus on the communication, the computation infrastructure or model development. To address this, we propose a new metric, the Energy Cost of AI lifecycle (eCAL). eCAL captures the energy consumption throughout the architectural components and lifecycle of an AI-powered wireless system by analyzing the complexity of data collection and manipulation in individual components and deriving overall and per-bit energy consumption. We show that the better a model and the more it is used, the more energy efficient an inference is. For an example Artificial Intelligence of Things (AIoT) configuration, eCAL for making 100 inferences is 2.73 times higher than for 1000 inferences. Additionally, we developed a modular open source simulation tool to enable researchers, practitioners, and engineers to calculate the end-to-end energy cost with various configurations and across various systems, ensuring adaptability to diverse use cases.