Mutations are the raw material of evolution but have been difficult to study directly. We report the largest study of new mutations to date, comprising 2,058 germline changes discovered by analyzing 85,289 Icelanders at 2,477 microsatellites. The paternal-to-maternal mutation rate ratio is 3.3, and the rate in fathers doubles from age 20 to 58, whereas there is no association with age in mothers. Longer microsatellite alleles are more mutagenic and tend to decrease in length, whereas the opposite is seen for shorter alleles. We use these empirical observations to build a model that we apply to individuals for whom we have both genome sequence and microsatellite data, allowing us to estimate key parameters of evolution without calibration to the fossil record. We infer that the sequence mutation rate is 1.4-2.3×10(-8) mutations per base pair per generation (90% credible interval) and that human-chimpanzee speciation occurred 3.7-6.6 million years ago.