Of signal interest in the genetics of traits are estimating the proportion, π 1 , of causally associated single nucleotide polymorphisms (SNPs), and their effect size variance, σ 2 β , which are components of the mean heritabilities captured by the causal SNP. Here we present the first model, using detailed linkage disequilibrium structure, to estimate these quantities from genome-wide association studies (GWAS) summary statistics, assuming a Gaussian distribution of SNP effect sizes, β. We apply the model to three diverse phenotypes -schizophrenia, putamen volume, and educational attainment -and validate it with extensive simulations. We find that schizophrenia is highly polygenic, with ≃ 5 × 10 4 causal SNPs distributed with small effect size variance, σ 2 β = 3.5 × 10 −5 (in units where the phenotype variance is normalized to 1), requiring a GWAS study with more than 1/2-million samples in each arm for full discovery. In contrast, putamen volume involves only ≃ 3 × 10 2 causal SNPs, but with σ 2 β = 1.2 × 10 −3 , indicating a much larger proportion of the causal SNPs that are strongly associated. Educational attainment has similar polygenicity to schizophrenia, but with effects that are substantially weaker, σ 2 β = 5 × 10 −6 , leading to much lower heritability. Thus the model is able to describe the broad genetic architecture of phenotypes where both polygenicity and effect size variance range over several orders of magnitude, shows why only small proportions of heritability have been explained for discovered SNPs, and provides a roadmap for future GWAS discoveries.