Reconstructing the DNA of ancestors from their descendants has the potential to empower phenotypic analyses (including association and genetic nurture studies), improve pedigree reconstruction, and shed light on the ancestral population and phenotypes of ancestors. We developed HAPI-RECAP, a method that reconstructs the DNA of parents from full siblings and their relatives. This tool leverages HAPI2's output, a new phasing approach that applies to siblings (and optionally one or both parents) and reliably infers parent haplotypes but does not link the ungenotyped parents' DNA across chromosomes or between segments flanking ambiguities. By combining IBD between the reconstructed parents and the relatives, HAPI-RECAP resolves the source parent of these segments. Moreover, the method exploits crossovers the children inherited and sex-specific genetic maps to infer the reconstructed parents' sexes. We validated these methods on research participants from both 23andMe, Inc. and the San Antonio Mexican American Family Studies. Given data for one parent, HAPI2 reconstructs large fractions of the missing parent's DNA, between 77.6% and 99.97% among all families, and 90.3% on average in three- and four-child families. When reconstructing both parents, HAPI-RECAP inferred between 33.2% and 96.6% of the parents' genotypes, averaging 70.6% in four-child families. Reconstructed genotypes have average error rates <10−3, or comparable to those from direct genotyping. HAPI-RECAP inferred the parent sexes 100% correctly given IBD-linked segments and can also reconstruct parents without any IBD. As datasets grow in size, more families will be implicitly collected; HAPI-RECAP holds promise to enable high quality parent genotype reconstruction.