You measure turn latency using the per-turn metrics field on each ChatMessage. The key value is e2e_latency, which represents the time from when the user stopped speaking to when the agent began responding. These metrics are available via session.history or the conversation_item_added event.
For deeper analysis, you can also inspect component-level metrics such as end-of-utterance delay, LLM time-to-first-token (TTFT), and TTS time-to-first-byte (TTFB). All of this is described in the Per-turn latency section of Data hooks.