Transformers are widely used for their ability to capture data relations in sequence processing, with great success for a wide range of static tasks. However, the computational and memory footprint of their main component, i.e., the Scaled Dot-product Attention, is commonly overlooked. This makes their adoption in applications involving stream data processing with constraints in response latency, computational and memory resources infeasible. Some works have proposed methods to lower the computational cost of Transformers, i.e. low-rank approximations, sparsity in attention, and efficient formulations for Continual Inference. In this paper, we introduce a new formulation of the Scaled Dot-product Attention based on the Nyström approximation that is suitable for Continual Inference. In experiments on Online Audio Classification and Online Action Detection tasks, the proposed Continual Scaled Dot-product Attention can lower the number of operations by up to three orders of magnitude compared to the original Transformers while retaining the predictive performance of competing models.