Reasoning large language models (LLMs) have demonstrated superior capacities in solving complicated problems by generating long chain-of-thoughts (CoT), but such a lengthy CoT incurs high inference costs. Previous methods on inference-stage efficient reasoning either require white-box models to monitor the reasoning process or are not reliable through direct prompting. In response, we introduce ES-CoT, an inference-time method that shortens CoT generation by detecting answer convergence and stopping early with almost no performance loss. When observing a linguistic marker (such as "wait") in the reasoning process, we prompt the LLM to output its current final answer, denoted as a step answer. We then track the run length of consecutive identical step answers as a measure of answer convergence. We show both empirically and theoretically that step answers steadily converge to the final answer, and large run-length jumps reliably mark this convergence. Experiments on six reasoning datasets across three LLMs show that ES-CoT reduces the number of inference tokens by 16.08% on average while maintaining accuracy comparable to standard CoT.