Unlike traditional text data, conversations are intricately structured through multiple turn-takings that shape their overall dynamics, and these dynamics are pivotal in defining the nature, effectiveness, and trajectory of the conversations. Traditional textual similarity measures, however, overlook this unique structure, often viewing conversations as sequences of utterances rather than evolving interactive processes. In this work, we present a new conversation-level similarity measure that captures the dynamics of a conversation. To validate our approach, we propose two validation methods that reliably generate conversation similarity labels using simulated conversations. We demonstrate the utility of our measure through multiple applications. We calculate between-group similarity and show how the conversational dynamics leading to toxicity have changed over time on a platform. We also use it as a distance metric for clustering in two settings—identifying different ways a conversation’s dynamics can progress toward being derailed into toxic behavior.