Analyses of data from genome-wide association studies on unrelated individuals have shown that, for human traits and diseases, approximately one-third to two-thirds of heritability is captured by common SNPs. However, it is not known whether the remaining heritability is due to the imperfect tagging of causal variants by common SNPs, in particular whether the causal variants are rare, or whether it is overestimated due to bias in inference from pedigree data. Here we estimated heritability for height and body mass index (BMI) from whole-genome sequence data on 25,465 unrelated individuals of European ancestry. The estimated heritability was 0.68 (standard error 0.10) for height and 0.30 (standard error 0.10) for body mass index. Low minor allele frequency variants in low linkage disequilibrium (LD) with neighboring variants were enriched for heritability, to a greater extent for protein-altering variants, consistent with negative selection. Our results imply that rare variants, in particular those in regions of low linkage disequilibrium, are a major source of the still missing heritability of complex traits and disease.