Distance Is All You Need: Radial Dispersion for Uncertainty Estimation in Large Language Models

Detecting when large language models (LLMs) are uncertain is critical for building reliable systems, yet existing methods are overly complicated, relying on brittle semantic clustering or internal states. We introduce \textbf{Radial Dispersion Score (RDS)}, a simple, parameter-free, fully model-agnostic uncertainty metric that measures the radial dispersion of sampled generations in embedding space. A lightweight probability-weighted variant further incorporates the model's own token probabilities when available, outperforming different nine strong baselines. Moroever, RDS naturally extends to per-sample scoring, enabling applications such as best-of-$N$ selection and confidence-based filtering. Across four challenging free-form QA datasets and multiple LLMs, our metrics achieve state-of-the-art hallucination detection and answer selection performance, while remaining robust and scalable with respect to sample size and embedding choice.