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The number of variants that have a non-zero effect on a trait (i.e. polygenicity) is a fundamental parameter in the study of the genetic architecture of a complex trait. Although many previous studies have investigated polygenicity at a genome-wide scale, a detailed understanding of how polygenicity varies across genomic regions is currently lacking. In this work, we propose an accurate and scalable statistical framework to estimate regional polygenicity for a complex trait. We show that our approach yields approximately unbiased estimates of regional polygenicity in simulations across a wide-range of various genetic architectures. We then partition the polygenicity of anthropometric and blood pressure traits across 6-Mb genomic regions (N = 290K, UK Biobank) and observe that all analyzed traits are highly polygenic: over one-third of regions harbor at least one causal variant for each of the traits analyzed. Additionally, we observe wide variation in regional polygenicity: on average across all traits, 48.9% of regions contain at least 5 causal SNPs, 5.44% of regions contain at least 50 causal SNPs. Finally, we find that heritability is proportional to polygenicity at the regional level, which is consistent with the hypothesis that heritability enrichments are largely driven by the variation in the number of causal SNPs.