Artificial intelligence (AI)coupled with existing Internet of Things (IoT) enables more streamlined and autonomous operations across various economic sectors. Consequently, the paradigm of Artificial Intelligence of Things (AIoT) having AI techniques at its core implies additional energy and carbon costs that may become significant with more complex neural architectures. To better understand the energy and Carbon Footprint (CF) of some AIoT components, very recent studies employ conventional metrics. However, these metrics are not designed to capture energy efficiency aspects of inference. In this paper, we propose a new metric, the Energy Cost of AIoT Lifecycle (eCAL) to capture the overall energy cost of inference over the lifecycle of an AIoT system. We devise a new methodology for determining eCAL of an AIoT system by analyzing the complexity of data manipulation in individual components involved in the AIoT lifecycle and derive the overall and per bit energy consumption. With eCAL we show that the better a model is and the more it is used, the more energy efficient an inference is. For an example AIoT configuration, eCAL for making $100$ inferences is $1.43$ times higher than for $1000$ inferences. We also evaluate the CF of the AIoT system by calculating the equivalent CO$_{2}$ emissions based on the energy consumption and the Carbon Intensity (CI) across different countries. Using 2023 renewable data, our analysis reveals that deploying an AIoT system in Germany results in emitting $4.62$ times higher CO$_2$ than in Finland, due to latter using more low-CI energy sources.

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