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SNP heritability, the proportion of phenotypic variation explained by genotyped SNPs, is an important parameter in understanding the genetic architecture underlying various diseases and traits. Methods that aim to estimate SNP heritability from individual genotype and phenotype data are limited by their ability to scale to Biobank-scale data sets and by the restrictions in access to individual-level data. These limitations have motivated the development of methods that only require summary statistics. Although the availability of publicly accessible summary statistics makes them widely applicable, these methods lack the accuracy of methods that utilize individual genotypes. Here we present a SUMmary-statistics-based Randomized Haseman-Elston regression (SUM-RHE), a method that can estimate the SNP heritability of complex phenotypes with accuracies comparable to approaches that require individual genotypes, while exclusively relying on summary statistics. SUM-RHE employs Genome-Wide Association Study (GWAS) summary statistics and statistics obtained on a reference population, which can be efficiently estimated and readily shared for public use. Our results demonstrate that SUM-RHE obtains estimates of SNP heritability that are substantially more accurate compared with other summary statistic methods and on par with methods that rely on individual-level data.