The number of de novo mutations (DNMs) in the human germline is correlated with parental age at conception, but this explains only part of the observed variation. We investigated whether there is a family-specific contribution to the number of DNMs in offspring. The analysis of DNMs in 111 dizygotic twin pairs did not identify a substantial family-specific contribution. This result was corroborated by comparing DNMs of 1669 siblings to those of age-matched unrelated offspring following correction for parental age. In addition, by modeling DNM data from 1714 multi-offspring families, we estimated that the family-specific contribution explains ∼5.2% of the variation in DNM number. Furthermore, we found no substantial difference between the observed number of DNMs and those predicted by a stochastic Poisson process. We conclude that there is a small family-specific contribution to DNM number and that stochasticity explains a large proportion of variation in DNM counts.